How to find an angle in a polygon - PSAT Math
Card 0 of 77
A regular polygon has a measure of 
for each of its internal angles. How many sides does it have?
A regular polygon has a measure of 
Tap to see back →
To determine the measure of the angles of a regular polygon use:
Angle = (n – 2) x 180° / n
Thus, (n – 2) x 180° / n = 140°
180° n - 360° = 140° n
40° n = 360°
n = 360° / 40° = 9
To determine the measure of the angles of a regular polygon use:
Angle = (n – 2) x 180° / n
Thus, (n – 2) x 180° / n = 140°
180° n - 360° = 140° n
40° n = 360°
n = 360° / 40° = 9
A regular seven sided polygon has a side length of 14”. What is the measurement of one of the interior angles of the polygon?
A regular seven sided polygon has a side length of 14”. What is the measurement of one of the interior angles of the polygon?
Tap to see back →
The formula for of interior angles based on a polygon with a number of side n is:
Each Interior Angle = (n-2)*180/n
= (7-2)*180/7 = 128.57 degrees
The formula for of interior angles based on a polygon with a number of side n is:
Each Interior Angle = (n-2)*180/n
= (7-2)*180/7 = 128.57 degrees
If angle A and angle C are complementary angles and B and D are supplementary angles, which of the following must be true?
If angle A and angle C are complementary angles and B and D are supplementary angles, which of the following must be true?
Tap to see back →
This question is very misleading, because while each answer COULD be true, none of them MUST be true. Between angle A and C, onne of the angles could be very small (0.001 degrees) and the other one could be very large. For instance, if A = 89.9999 and C = 0.0001, AC = 0.009. On the other hand, the two angles could be very siimilar. If B = 90 and D = 90 then BD = 8100 and BD > AC. If we use these same values we disprove AD = BC as 8100 ≠ .009. Finally, if B is a very small value, then B/C will be very small and smaller than A/D.
This question is very misleading, because while each answer COULD be true, none of them MUST be true. Between angle A and C, onne of the angles could be very small (0.001 degrees) and the other one could be very large. For instance, if A = 89.9999 and C = 0.0001, AC = 0.009. On the other hand, the two angles could be very siimilar. If B = 90 and D = 90 then BD = 8100 and BD > AC. If we use these same values we disprove AD = BC as 8100 ≠ .009. Finally, if B is a very small value, then B/C will be very small and smaller than A/D.
In isosceles triangle ABC, the measure of angle A is 50 degrees. Which is NOT a possible measure for angle B?
In isosceles triangle ABC, the measure of angle A is 50 degrees. Which is NOT a possible measure for angle B?
Tap to see back →
If angle A is one of the base angles, then the other base angle must measure 50 degrees. Since 50 + 50 + x = 180 means x = 80, the vertex angle must measure 80 degrees.
If angle A is the vertex angle, the two base angles must be equal. Since 50 + x + x = 180 means x = 65, the two base angles must measure 65 degrees.
The only number given that is not possible is 95 degrees.
If angle A is one of the base angles, then the other base angle must measure 50 degrees. Since 50 + 50 + x = 180 means x = 80, the vertex angle must measure 80 degrees.
If angle A is the vertex angle, the two base angles must be equal. Since 50 + x + x = 180 means x = 65, the two base angles must measure 65 degrees.
The only number given that is not possible is 95 degrees.
In triangle ABC, the measure of angle A = 70 degrees, the measure of angle B = x degrees, and the measure of angle C = y degrees. What is the value of y in terms of x?
In triangle ABC, the measure of angle A = 70 degrees, the measure of angle B = x degrees, and the measure of angle C = y degrees. What is the value of y in terms of x?
Tap to see back →
Since the three angles of a triangle sum to 180, we know that 70 + x + y = 180. Subtract 70 from both sides and see that x + y = 110. Subtract x from both sides and see that y = 110 – x.
Since the three angles of a triangle sum to 180, we know that 70 + x + y = 180. Subtract 70 from both sides and see that x + y = 110. Subtract x from both sides and see that y = 110 – x.
What is the measure, in degrees, of each interior angle of a regular convex polygon that has twelve sides?
What is the measure, in degrees, of each interior angle of a regular convex polygon that has twelve sides?
Tap to see back →
The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180(n – 2), where n is the number of sides. The problem concerns a polygon with twelve sides, so we will let n = 12. The sum of the interior angles in this polygon would be 180(12 – 2) = 180(10) = 1800.
Because the polygon is regular (meaning its sides are all congruent), all of the angles have the same measure. Thus, if we divide the sum of the measures of the angles by the number of sides, we will have the measure of each interior angle. In short, we need to divide 1800 by 12, which gives us 150.
The answer is 150.
The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180(n – 2), where n is the number of sides. The problem concerns a polygon with twelve sides, so we will let n = 12. The sum of the interior angles in this polygon would be 180(12 – 2) = 180(10) = 1800.
Because the polygon is regular (meaning its sides are all congruent), all of the angles have the same measure. Thus, if we divide the sum of the measures of the angles by the number of sides, we will have the measure of each interior angle. In short, we need to divide 1800 by 12, which gives us 150.
The answer is 150.
In the figure above, polygon ABDFHGEC is a regular octagon. What is the measure, in degrees, of angle FHI?
In the figure above, polygon ABDFHGEC is a regular octagon. What is the measure, in degrees, of angle FHI?
Tap to see back →
Angle FHI is the supplement of angle FHG, which is an interior angle in the octagon. When two angles are supplementary, their sum is equal to 180 degrees. If we can find the measure of each interior angle in the octagon, then we can find the supplement of angle FHG, which will give us the measure of angle FHI.
The sum of the interior angles in a regular polygon is given by the formula 180(n – 2), where n is the number of sides in the polygon. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees. Because the octagon is regular, all of its sides and angles are congruent. Thus, the measure of each angle is equal to the sum of its angles divided by 8. Therefore, each angle in the polygon has a measure of 1080/8 = 135 degrees. This means that angle FHG has a measure of 135 degrees.
Now that we know the measure of angle FHG, we can find the measure of FHI. The sum of the measures of FHG and FHI must be 180 degrees, because the two angles form a line and are supplementary. We can write the following equation:
Measure of FHG + measure of FHI = 180
135 + measure of FHI = 180
Subtract 135 from both sides.
Measure of FHI = 45 degrees.
The answer is 45.
Angle FHI is the supplement of angle FHG, which is an interior angle in the octagon. When two angles are supplementary, their sum is equal to 180 degrees. If we can find the measure of each interior angle in the octagon, then we can find the supplement of angle FHG, which will give us the measure of angle FHI.
The sum of the interior angles in a regular polygon is given by the formula 180(n – 2), where n is the number of sides in the polygon. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees. Because the octagon is regular, all of its sides and angles are congruent. Thus, the measure of each angle is equal to the sum of its angles divided by 8. Therefore, each angle in the polygon has a measure of 1080/8 = 135 degrees. This means that angle FHG has a measure of 135 degrees.
Now that we know the measure of angle FHG, we can find the measure of FHI. The sum of the measures of FHG and FHI must be 180 degrees, because the two angles form a line and are supplementary. We can write the following equation:
Measure of FHG + measure of FHI = 180
135 + measure of FHI = 180
Subtract 135 from both sides.
Measure of FHI = 45 degrees.
The answer is 45.
What is the measure of each angle in a regular octagon?
What is the measure of each angle in a regular octagon?
Tap to see back →
An octagon contains six triangles, or 1080 degrees. This means with 8 angles, each angle is 135 degrees.
An octagon contains six triangles, or 1080 degrees. This means with 8 angles, each angle is 135 degrees.
What is the measure of each central angle of an octagon?
What is the measure of each central angle of an octagon?
Tap to see back →
There are 360 degrees and 8 angles, so dividing leaves 45 degrees per angle.
There are 360 degrees and 8 angles, so dividing leaves 45 degrees per angle.
Note: Figure NOT drawn to scale.
Refer to the above figure. 
is equilateral and Pentagon 
is regular.
Evaluate 
.
Note: Figure NOT drawn to scale.
Refer to the above figure.
Evaluate
Tap to see back →
By angle addition,
is an angle of a reguar pentagon, so its measure is 
.
To find 
, first we find 
.
By angle addition,
is an angle of a regular pentagon and has measure 
.
, as an angle of an equilateral triangle, has measure 
.
is equilateral, so 
; Pentagon 
is regular, so 
. Therefore, 
, and by the Isosceles Triangle Theorem, 
.
The degree measures of three angles of a triangle total 
, so:
Since
we have
By angle addition,
To find
By angle addition,
The degree measures of three angles of a triangle total
Since
we have
Pentagon 
is regular. If diagonal 
is drawn, which of the following describes Quadrilateral 
?
Pentagon
Tap to see back →
The figure described is below.
Each of the angles of the pentagon has measure 
is an isosceles triangle, and 
, so
and
Since
,
and by the parallel postulate,
Quadrilateral 
has exactly one pair of parallel sides, so it is a trapezoid.
The figure described is below.
Each of the angles of the pentagon has measure
and
Since
and by the parallel postulate,
Quadrilateral
A regular polygon has a measure of for each of its internal angles. How many sides does it have?
A regular polygon has a measure of
Tap to see back →
To determine the measure of the angles of a regular polygon use:
Angle = (n – 2) x 180° / n
Thus, (n – 2) x 180° / n = 140°
180° n - 360° = 140° n
40° n = 360°
n = 360° / 40° = 9
To determine the measure of the angles of a regular polygon use:
Angle = (n – 2) x 180° / n
Thus, (n – 2) x 180° / n = 140°
180° n - 360° = 140° n
40° n = 360°
n = 360° / 40° = 9
A regular seven sided polygon has a side length of 14”. What is the measurement of one of the interior angles of the polygon?
A regular seven sided polygon has a side length of 14”. What is the measurement of one of the interior angles of the polygon?
Tap to see back →
The formula for of interior angles based on a polygon with a number of side n is:
Each Interior Angle = (n-2)*180/n
= (7-2)*180/7 = 128.57 degrees
The formula for of interior angles based on a polygon with a number of side n is:
Each Interior Angle = (n-2)*180/n
= (7-2)*180/7 = 128.57 degrees
If angle A and angle C are complementary angles and B and D are supplementary angles, which of the following must be true?
If angle A and angle C are complementary angles and B and D are supplementary angles, which of the following must be true?
Tap to see back →
This question is very misleading, because while each answer COULD be true, none of them MUST be true. Between angle A and C, onne of the angles could be very small (0.001 degrees) and the other one could be very large. For instance, if A = 89.9999 and C = 0.0001, AC = 0.009. On the other hand, the two angles could be very siimilar. If B = 90 and D = 90 then BD = 8100 and BD > AC. If we use these same values we disprove AD = BC as 8100 ≠ .009. Finally, if B is a very small value, then B/C will be very small and smaller than A/D.
This question is very misleading, because while each answer COULD be true, none of them MUST be true. Between angle A and C, onne of the angles could be very small (0.001 degrees) and the other one could be very large. For instance, if A = 89.9999 and C = 0.0001, AC = 0.009. On the other hand, the two angles could be very siimilar. If B = 90 and D = 90 then BD = 8100 and BD > AC. If we use these same values we disprove AD = BC as 8100 ≠ .009. Finally, if B is a very small value, then B/C will be very small and smaller than A/D.
In isosceles triangle ABC, the measure of angle A is 50 degrees. Which is NOT a possible measure for angle B?
In isosceles triangle ABC, the measure of angle A is 50 degrees. Which is NOT a possible measure for angle B?
Tap to see back →
If angle A is one of the base angles, then the other base angle must measure 50 degrees. Since 50 + 50 + x = 180 means x = 80, the vertex angle must measure 80 degrees.
If angle A is the vertex angle, the two base angles must be equal. Since 50 + x + x = 180 means x = 65, the two base angles must measure 65 degrees.
The only number given that is not possible is 95 degrees.
If angle A is one of the base angles, then the other base angle must measure 50 degrees. Since 50 + 50 + x = 180 means x = 80, the vertex angle must measure 80 degrees.
If angle A is the vertex angle, the two base angles must be equal. Since 50 + x + x = 180 means x = 65, the two base angles must measure 65 degrees.
The only number given that is not possible is 95 degrees.
In triangle ABC, the measure of angle A = 70 degrees, the measure of angle B = x degrees, and the measure of angle C = y degrees. What is the value of y in terms of x?
In triangle ABC, the measure of angle A = 70 degrees, the measure of angle B = x degrees, and the measure of angle C = y degrees. What is the value of y in terms of x?
Tap to see back →
Since the three angles of a triangle sum to 180, we know that 70 + x + y = 180. Subtract 70 from both sides and see that x + y = 110. Subtract x from both sides and see that y = 110 – x.
Since the three angles of a triangle sum to 180, we know that 70 + x + y = 180. Subtract 70 from both sides and see that x + y = 110. Subtract x from both sides and see that y = 110 – x.
What is the measure, in degrees, of each interior angle of a regular convex polygon that has twelve sides?
What is the measure, in degrees, of each interior angle of a regular convex polygon that has twelve sides?
Tap to see back →
The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180(n – 2), where n is the number of sides. The problem concerns a polygon with twelve sides, so we will let n = 12. The sum of the interior angles in this polygon would be 180(12 – 2) = 180(10) = 1800.
Because the polygon is regular (meaning its sides are all congruent), all of the angles have the same measure. Thus, if we divide the sum of the measures of the angles by the number of sides, we will have the measure of each interior angle. In short, we need to divide 1800 by 12, which gives us 150.
The answer is 150.
The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180(n – 2), where n is the number of sides. The problem concerns a polygon with twelve sides, so we will let n = 12. The sum of the interior angles in this polygon would be 180(12 – 2) = 180(10) = 1800.
Because the polygon is regular (meaning its sides are all congruent), all of the angles have the same measure. Thus, if we divide the sum of the measures of the angles by the number of sides, we will have the measure of each interior angle. In short, we need to divide 1800 by 12, which gives us 150.
The answer is 150.
In the figure above, polygon ABDFHGEC is a regular octagon. What is the measure, in degrees, of angle FHI?
In the figure above, polygon ABDFHGEC is a regular octagon. What is the measure, in degrees, of angle FHI?
Tap to see back →
Angle FHI is the supplement of angle FHG, which is an interior angle in the octagon. When two angles are supplementary, their sum is equal to 180 degrees. If we can find the measure of each interior angle in the octagon, then we can find the supplement of angle FHG, which will give us the measure of angle FHI.
The sum of the interior angles in a regular polygon is given by the formula 180(n – 2), where n is the number of sides in the polygon. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees. Because the octagon is regular, all of its sides and angles are congruent. Thus, the measure of each angle is equal to the sum of its angles divided by 8. Therefore, each angle in the polygon has a measure of 1080/8 = 135 degrees. This means that angle FHG has a measure of 135 degrees.
Now that we know the measure of angle FHG, we can find the measure of FHI. The sum of the measures of FHG and FHI must be 180 degrees, because the two angles form a line and are supplementary. We can write the following equation:
Measure of FHG + measure of FHI = 180
135 + measure of FHI = 180
Subtract 135 from both sides.
Measure of FHI = 45 degrees.
The answer is 45.
Angle FHI is the supplement of angle FHG, which is an interior angle in the octagon. When two angles are supplementary, their sum is equal to 180 degrees. If we can find the measure of each interior angle in the octagon, then we can find the supplement of angle FHG, which will give us the measure of angle FHI.
The sum of the interior angles in a regular polygon is given by the formula 180(n – 2), where n is the number of sides in the polygon. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees. Because the octagon is regular, all of its sides and angles are congruent. Thus, the measure of each angle is equal to the sum of its angles divided by 8. Therefore, each angle in the polygon has a measure of 1080/8 = 135 degrees. This means that angle FHG has a measure of 135 degrees.
Now that we know the measure of angle FHG, we can find the measure of FHI. The sum of the measures of FHG and FHI must be 180 degrees, because the two angles form a line and are supplementary. We can write the following equation:
Measure of FHG + measure of FHI = 180
135 + measure of FHI = 180
Subtract 135 from both sides.
Measure of FHI = 45 degrees.
The answer is 45.
What is the measure of each angle in a regular octagon?
What is the measure of each angle in a regular octagon?
Tap to see back →
An octagon contains six triangles, or 1080 degrees. This means with 8 angles, each angle is 135 degrees.
An octagon contains six triangles, or 1080 degrees. This means with 8 angles, each angle is 135 degrees.
What is the measure of each central angle of an octagon?
What is the measure of each central angle of an octagon?
Tap to see back →
There are 360 degrees and 8 angles, so dividing leaves 45 degrees per angle.
There are 360 degrees and 8 angles, so dividing leaves 45 degrees per angle.