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High School Math : How to find an angle in an acute / obtuse triangle

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Example Questions

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

Solve for . (Not drawn to scale).

Possible Answers:

57^o

22^o

81^o

53^o

Correct answer:

53^o

Explanation:

The angles of a triangle must add to 180^o. In the triangle to the right, we know one angle and can find another using supplementary angles.

57+(180-110)+x=180

Now we only need to solve for .

57+70+x=180

x=180-(57+70)=180-127

x=53^o

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Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

Exterior_angle If $\angle A=42^{\circ}$ and $\angle B=76^{\circ}$ , what is the measure of $\theta$ ?

Possible Answers:

$62^{\circ}$

$76^{\circ}$

$118^{\circ}$

$42^{\circ}$

Not enough information to solve

Correct answer:

$118^{\circ}$

Explanation:

All of the interior angles of a triangle add up to $180^{\circ}$ .

If $\angle A=42^{\circ}$ and $\angle B=76^{\circ}$ , then

$\angle C= 180^{\circ}-(42^{\circ}+76^{\circ})$

Therefore, $\angle C=62^{\circ}$

Now, $\theta$ will equal $180^{\circ}-\angle C$ because $\angle C$ and $\theta$ form a straight line. Therefore,

$\theta=180^{\circ}-62^{\circ}$

$\rightarrow118^{\circ}$

Also, by definition, the angle of an exterior angle of a triangle is equal to the measure of the two interior angles opposite of it $\dpi{100} (\theta =76^{\circ}+42^{\circ}\rightarrow 118^{\circ})$ .

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Example Question #2 : Acute / Obtuse Triangles

Two interior angles in an obtuse triangle measure $123^{\circ}$ and $11^{\circ}$ . What is the measurement of the third angle.

Possible Answers:

$123^{\circ}$

$46^{\circ}$

$104^{\circ}$

$50^{\circ}$

$57^{\circ}$

Correct answer:

$46^{\circ}$

Explanation:

Interior angles of a triangle always add up to 180 degrees.

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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 #4 : Isosceles Triangles

Triangle ABC has angle measures as follows:

$\dpi{100} \small m\angle ABC=4x+3$

$\dpi{100} \small m\angle ACB=2x+6$

$\dpi{100} \small m\angle BAC=3x$

What is $\dpi{100} \small m\angle BAC$ ?

Possible Answers:

Correct answer:

Explanation:

The sum of the measures of the angles of a triangle is 180.

Thus we set up the equation $\dpi{100} \small 4x+3+2x+6+3x=180$

After combining like terms and cancelling, we have $\dpi{100} \small 9x=171\rightarrow x=19$

Thus $\dpi{100} \small m\angle BAC=3x=57$

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Example Question #5 : Isosceles Triangles

The base angle of an isosceles triangle is five more than twice the vertex angle. What is the base angle?

Possible Answers:

$62$

$34$

$47$

$55$

$73$

Correct answer:

$73$

Explanation:

Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let $x$ = the vertex angle and $2x+5$ = the base angle

So the equation to solve becomes $x+(2x+5)+(2x+5)=180$

Thus the vertex angle is 34 and the base angles are 73.

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Example Question #6 : Isosceles Triangles

The base angle of an isosceles triangle is 15 less than three times the vertex angle. What is the vertex angle?

Possible Answers:

Correct answer:

Explanation:

Every triangle contains 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let = vertex angle and 3x-15 = base angle

So the equation to solve becomes x+(3x-15)+(3x-15)=180 .

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Example Question #4 : Isosceles Triangles

The base angle of an isosceles triangle is ten less than twice the vertex angle. What is the vertex angle?

Possible Answers:

$70^{\circ}$

$35^{\circ}$

$20^{\circ}$

$40^{\circ}$

$65^{\circ}$

Correct answer:

$40^{\circ}$

Explanation:

Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let = vertex angle and 2x - 10 = base angle

So the equation to solve becomes x + (2x - 10) + (2x - 10) = 180

So the vertex angle is 40 and the base angles is 70

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Example Question #5 : How To Find An Angle In An Acute / Obtuse Triangle

The base angle of an isosceles triangle is 10 more than twice the vertex angle. What is the vertex angle?

Possible Answers:

$60^{\circ}$

$50^{\circ}$

$32^{\circ}$

$74^{\circ}$

$45^{\circ}$

Correct answer:

$32^{\circ}$

Explanation:

Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let = the vertex angle and 2x + 10 = the base angle

So the equation to solve becomes x + (2x +10) + (2x +10) = 180

The vertex angle is 32 degrees and the base angle is 74 degrees

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Example Question #6 : How To Find An Angle In An Acute / Obtuse Triangle

In an isosceles triangle, the vertex angle is 15 less than the base angle. What is the base angle?

Possible Answers:

Correct answer:

Explanation:

Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let = base angle and x - 15 = vertex angle

So the equation to solve becomes (x - 15) + x + x = 180

Thus, 65 is the base angle and 50 is the vertex angle.

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High School Math : How to find an angle in an acute / obtuse triangle

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #2 : Acute / Obtuse Triangles

Example Question #1 : Acute / Obtuse Triangles

Example Question #4 : Isosceles Triangles

Example Question #5 : Isosceles Triangles

Example Question #6 : Isosceles Triangles

Example Question #4 : Isosceles Triangles

Example Question #5 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #6 : How To Find An Angle In An Acute / Obtuse Triangle

All High School Math Resources

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