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GED Math : Angles and Triangles

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Example Question #1 : Angles And Triangles

Which of the following can be the measures of the three angles of an acute isosceles triangle?

Possible Answers:

$45 ^{\circ }, 45 ^{\circ }, 90^{\circ }$

$80 ^{\circ }, 80 ^{\circ }, 40 ^{\circ }$

$32 ^{\circ }, 32 ^{\circ }, 116^{\circ }$

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$

$50 ^{\circ }, 60 ^{\circ }, 70 ^{\circ }$

Correct answer:

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$

Explanation:

For the triangle to be acute, all three angles must measure less than $90 ^{\circ }$ . We can eliminate $32 ^{\circ }, 32 ^{\circ }, 116^{\circ }$ and $45 ^{\circ }, 45 ^{\circ }, 90^{\circ }$ for this reason.

In an isosceles triangle, at least two angles are congruent, so we can eliminate $50 ^{\circ }, 60 ^{\circ }, 70 ^{\circ }$ .

The degree measures of the three angles of a triangle must total 180, so, since $80 ^{\circ }+ 80 ^{\circ }+ 40 ^{\circ } = 200^{\circ }$ , we can eliminate $80 ^{\circ }, 80 ^{\circ }, 40 ^{\circ }$ .

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$ is correct.

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Example Question #2 : Angles And Triangles

Triangle

Note: Figure NOT drawn to scale.

Refer to the above triangle. Evaluate .

Possible Answers:

x = 51

x = 31

x = 39

x = 63

Correct answer:

x = 39

Explanation:

The degree measures of a triangle total $180^{\circ }$ , so

x + (x+24) + 2x = 180

4x+24 = 180

4x+24 -24 = 180 -24

4x = 156

$4x \div 4 = 156 \div 4$

x = 39

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Example Question #3 : Angles And Triangles

Triangle

Note: Figure NOT drawn to scale.

Refer to the above figure. Evaluate .

Possible Answers:

$y = 56 \frac{1}{2}$

y = 41

$y = 20 \frac{1}{2}$

y = 31

Correct answer:

$y = 56 \frac{1}{2}$

Explanation:

The degree measures of the interior angles of a triangle total $180 ^{\circ }$ , so, if we let $x^{\circ }$ be the measure of the unmarked angle, then

x + 41 + 72 = 180

x + 113 = 180

x = 67

Three angles with measures $67^{\circ}, y^{\circ}, y^{\circ}$ together form a straight angle, so

y+ y + 67= 180

2y+ 67= 180

2y+ 67- 67 = 180 - 67

2y = 113

$2y \div 2 = 113 \div 2$

$y = 56 \frac{1}{2}$

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Example Question #1 : Angles And Triangles

Thingy

Figure drawn to scale.

Refer to the above diagram.

Which of the following is a valid description of $\Delta EFC$ ?

Possible Answers:

Acute

Obtuse

Equiangular

Right

Correct answer:

Obtuse

Explanation:

One of the angles of $\Delta EFC$ - namely, $\angle EFC$ - can be seen to be an obtuse angle, as it is wider than a right angle. This makes $\Delta EFC$ , by definition, an obtuse triangle.

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Example Question #5 : Angles And Triangles

Thingy

Refer to the above diagram.

Which of the following is a valid description of $\Delta CED$ ?

Possible Answers:

Equiangular

Right

Acute

Obtuse

Correct answer:

Right

Explanation:

One of the angles of $\Delta CED$ - namely, $\angle CDE$ - is marked as a right angle. This makes $\Delta CED$ , by definition, a right triangle.

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Example Question #6 : Angles And Triangles

Which of the following follows from the fact that $\Delta MNO \cong \Delta PQR$ ?

Possible Answers:

$\angle M \cong \angle P$

$\angle O \cong \angle Q$

$\angle M \cong \angle N$

$\angle N \cong \angle R$

Correct answer:

$\angle M \cong \angle P$

Explanation:

A congruency statement about two triangles implies nothing about the relationship between two angles of one of the triangles, so $\angle M \cong \angle N$ is not correct.

Also, letters in the same position between the two triangles refer to corresponding - and subsequently, congruent - angles. Therefore, $\Delta MNO \cong \Delta PQR$ implies that:

$\angle M \cong \angle P$

$\angle N \cong \angle Q$

$\angle O \cong \angle R$

Of the given choices, only $\angle M \cong \angle P$ is a consequence. It is the correct response.

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Example Question #7 : Angles And Triangles

An exterior angle of an isosceles triangle measures $130 ^{\circ }$ . What is the greatest measure of any of the three angles of the triangle?

Possible Answers:

$65 ^{\circ }$

$50^{\circ }$

Insufficient information is given to answer this question.

$80 ^{\circ }$

Correct answer:

Insufficient information is given to answer this question.

Explanation:

The triangle has an exterior angle of $130 ^{\circ }$ , so it has an interior angle of $(180-130)^{\circ } = 50^{\circ }$ . By the Isosceles Triangle Theorem, an isosceles triangle must have two congruent angles; there are two possible scenarios that fit this criterion:

Case 1: Two angles have measure $50^{\circ }$ . The third angle will have measure

$\left [180 - (50 + 50 ) \right ] ^{\circ } = 80 ^{\circ }$ .

$80 ^{\circ }$ will be the greatest of the angle measures.

Case 2: One angle has measure $50^{\circ }$ and the others are congruent. Their common measure will be

$\frac{1}{2} (180^{\circ }- 50^{\circ } ) = 65 ^{\circ }$ .

$65 ^{\circ }$ will be the greatest of the angle measures.

The given information is therefore inconclusive.

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Example Question #8 : Angles And Triangles

An exterior angle of an isosceles triangle measures $130 ^{\circ }$ . What is the least measure of any of the three angles of the triangle?

Possible Answers:

$50^{\circ }$

$65 ^{\circ }$

$80 ^{\circ }$

Insufficient information is given to answer this question

Correct answer:

$50^{\circ }$

Explanation:

Case 1: Two angles have measure $50^{\circ }$ . The third angle will have measure

$\left [180 - (50 + 50 ) \right ] ^{\circ } = 80 ^{\circ }$ .

$50^{\circ }$ will be the least of the angle measures.

Case 2: One angle has measure $50^{\circ }$ and the others are congruent. Their common measure will be

$\frac{1}{2} (180^{\circ }- 50^{\circ } ) = 65 ^{\circ }$ .

$50^{\circ }$ will be the least of the angle measures.

In both cases, the least of the degree measures of the angles will be $50^{\circ }$ .

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Example Question #9 : Angles And Triangles

An exterior angle of an isosceles triangle measures $70 ^{\circ }$ . What is the least measure of any of the three angles of the triangle?

Possible Answers:

$70^{\circ }$

$40^{\circ }$

$35 ^{\circ }$

Insufficient information is given to answer this question.

Correct answer:

$35 ^{\circ }$

Explanation:

The triangle has an exterior angle of $70 ^{\circ }$ , so it has an interior angle of $(180-70)^{\circ } = 110 ^{\circ }$ .

Since this is an obtuse angle, its other two angles must be acute. By the Isosceles Triangle Theorem, an isosceles triangle must have two congruent angles - the acute angles are those. Since the sum of their measures is the same as their remote exterior angle - $70 ^{\circ }$ - each has measure $35 ^{\circ }$ .This is the correct response.

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Example Question #2 : Angles And Triangles

An exterior angle of an isosceles triangle measures $80 ^{\circ }$ . What is the greatest measure of any of the three angles of the triangle?

Possible Answers:

$80^{\circ }$

Insufficient information is given to answer this question.

$40^{\circ }$

$100 ^{\circ }$

Correct answer:

$100 ^{\circ }$

Explanation:

The triangle has an exterior angle of $80 ^{\circ }$ , so it has an interior angle of $(180-80)^{\circ } = 100 ^{\circ }$ .

Since this is an obtuse angle, its other two angles must be acute. Therefore, this angle is the one of greatest measure.

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GED Math : Angles and Triangles

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1 : Angles And Triangles

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Example Question #3 : Angles And Triangles

Example Question #1 : Angles And Triangles

Example Question #5 : Angles And Triangles

Example Question #6 : Angles And Triangles

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