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HSPT Math : How to find the measure of an angle

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Example Questions

Example Question #1 : How To Find The Measure Of An Angle

What is the sum of the interior angles of a triangle?

Possible Answers:

180

270

360

Correct answer:

180

Explanation:

The sum of the three interior angles of a triangle is 180 degrees.

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Example Question #1 : How To Find The Measure Of An Angle

Two of the interior angles of a triangle measure $50^{\circ }$ and $45^{\circ}$ . What is the greatest measure of any of its exterior angles?

Possible Answers:

$135^{\circ }$

$85^{\circ }$

It cannot be determined from the information given.

$130^{\circ }$

$95^{\circ }$

Correct answer:

$135^{\circ }$

Explanation:

The interior angles of a triangle must have measures whose sum is $180^{\circ }$ , so the measure of the third angle must be $180 - (50+45) = 85^{\circ }$ .

By the Triangle Exterior-Angle Theorem, an exterior angle of a triangle measures the sum of its remote interior angles; therefore, to get the greatest measure of any exterior angle, we add the two greatest interior angle measures: $50+85= 135^{\circ }$

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Example Question #1 : How To Find An Angle Of A Line

Two angles are supplementary and have a ratio of 1:4. What is the size of the smaller angle?

Possible Answers:

$45^{\circ}$

$72^{\circ}$

$144^{\circ}$

$36^{\circ}$

$18^{\circ}$

Correct answer:

$36^{\circ}$

Explanation:

Since the angles are supplementary, their sum is 180 degrees. Because they are in a ratio of 1:4, the following expression could be written:

$x+4x=180$

$5x=180$

$x=36^{\circ}$

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Example Question #1 : Acute / Obtuse Triangles

In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?

Possible Answers:

$45^{\circ}$

$60^{\circ}$

$75^{\circ}$

$20^{\circ}$

$90^{\circ}$

Correct answer:

$60^{\circ}$

Explanation:

Since the sum of the angles of a triangle is $180^{\circ}$ , and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be , then the following expression could be written:

$x+3x+5x=180$

$9x=180$

$x=20$

If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.

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Example Question #1 : Right Triangles

The measure of 3 angles in a triangle are in a 1:2:3 ratio. What is the measure of the middle angle?

Possible Answers:

Correct answer: 60

Explanation:

The angles in a triangle sum to 180 degrees. This makes the middle angle 60 degrees.

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Example Question #3 : How To Find The Measure Of An Angle

Call the three angles of a triangle $\angle 1, \angle 2, \angle 3$ .

The measure of $\angle2$ is twenty degrees greater than that of $\angle 1$ ; the measure of $\angle 3$ is thirty degrees less than twice that of $\angle 1$ . If is the measure of $\angle 1$ , then which of the following equations would we need to solve in order to calculate the measures of the angles?

Possible Answers:

x + (x+20) = (2x+30)

x + (x-20) + 2(x-30) = 180

x + (x+20) + (2x-30) = 360

x + (x-20) + 2(x-30) = 360

x + (x+20) + (2x-30) = 180

Correct answer:

x + (x+20) + (2x-30) = 180

Explanation:

The measure of $\angle2$ is twenty degrees greater than the measure of $\angle 1$ , so its measure is 20 added to that of $\angle 1$ - that is, x + 2 0 .

The measure of $\angle 3$ is thirty degrees less than twice that of $\angle 1$ . Twice the measure of $\angle 1$ is , and thirty degrees less than this is 30 subtracted from - that is, 2x-30 .

The sum of the measures of the three angles of a triangle is 180, so, to solve for - thereby allowing us to calulate all three angle measures - we add these three expressions and set the sum equal to 180. This yields the equation:

x + (x+20) + (2x-30) = 180

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Example Question #4 : How To Find The Measure Of An Angle

Call the three angles of a triangle $\angle 1, \angle 2, \angle 3$ .

The measure of $\angle2$ is forty degrees less than that of $\angle 1$ ; the measure of $\angle 3$ is ten degrees less than twice that of $\angle 1$ . If is the measure of $\angle 1$ , then which of the following equations would we need to solve in order to calculate the measures of the angles?

Possible Answers:

x + (x-40) + 2 (x - 10) = 180

x + (x-40) + (2x - 10) = 360

x + (x-40) = (2x - 10)

x + (x-40) + 2 (x - 10) = 360

x + (x-40) + (2x - 10) = 180

Correct answer:

x + (x-40) + (2x - 10) = 180

Explanation:

The measure of $\angle2$ is forty degrees less than the measure of $\angle 1$ , so its measure is 40 subtracted from that of $\angle 1$ - that is, x -40 .

The measure of $\angle 3$ is ten degrees less than twice that of $\angle 1$ . Twice the measure of $\angle 1$ is , and ten degrees less than this is 10 subtracted from - that is, 2x-10 .

x + (x-40) + (2x - 10) = 180

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Example Question #4 : How To Find The Measure Of An Angle

Two interior angles of a triangle adds up to degrees. What is the measure of the other angle?

Possible Answers:

148

116

Correct answer:

116

Explanation:

The sum of the three angles of a triangle add up to 180 degrees. Subtract 64 degrees to determine the third angle.

180-64= 116

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Example Question #1 : How To Find The Measure Of An Angle

What is $\frac{1}{5}$ of the measure of a right angle?

Possible Answers:

$18$^{\circ}$$

$45$^{\circ}$$

$450$^{\circ}$$

$85$^{\circ}$$

$22$^{\circ}$$

Correct answer:

$18$^{\circ}$$

Explanation:

A right angle has a measure of $90$^{\circ}$$ . One fifth of the angle is:

$\angle A=\frac{90}{5}= 18$^{\circ}$$

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Example Question #6 : How To Find The Measure Of An Angle

What angle is complementary to $65$^{\circ}$$ ?

Possible Answers:

$130$^{\circ}$$

$25$^{\circ}$$

$115$^{\circ}$$

$65$^{\circ}$$

$35$^{\circ}$$

Correct answer:

$25$^{\circ}$$

Explanation:

To find the other angle, subtract the given angle from $90$^{\circ}$$ since complementary angles add up to $90$^{\circ}$$ .

The complementary is:

$\angle 90-\angle65 = \angle25$

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HSPT Math : How to find the measure of an angle

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1 : How To Find The Measure Of An Angle

Example Question #1 : How To Find The Measure Of An Angle

Example Question #1 : How To Find An Angle Of A Line

Example Question #1 : Acute / Obtuse Triangles

Example Question #1 : Right Triangles

Example Question #3 : How To Find The Measure Of An Angle

Example Question #4 : How To Find The Measure Of An Angle

Example Question #4 : How To Find The Measure Of An Angle

Example Question #1 : How To Find The Measure Of An Angle

Example Question #6 : How To Find The Measure Of An Angle

All HSPT Math Resources

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