# GED Math : Angles and Triangles

## Example Questions

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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?

Explanation:

For the triangle to be acute, all three angles must measure less than . We can eliminate  and  for this reason.

In an isosceles triangle, at least two angles are congruent, so we can eliminate .

The degree measures of the three angles of a triangle must total 180, so, since , we can eliminate .

is correct.

### Example Question #2 : Angles And Triangles

Note: Figure NOT drawn to scale.

Refer to the above triangle. Evaluate .

Explanation:

The degree measures of a triangle total , so

### Example Question #3 : Angles And Triangles

Note: Figure NOT drawn to scale.

Refer to the above figure. Evaluate .

Explanation:

The degree measures of the interior angles of a triangle total , so, if we let  be the measure of the unmarked angle, then

Three angles with measures  together form a straight angle, so

### Example Question #3 : Angles And Triangles

Figure drawn to scale.

Refer to the above diagram.

Which of the following is a valid description of  ?

Equiangular

Right

Acute

Obtuse

Obtuse

Explanation:

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

### Example Question #61 : Triangles

Refer to the above diagram.

Which of the following is a valid description of  ?

Obtuse

Acute

Right

Equiangular

Right

Explanation:

One of the angles of  - namely,  - is marked as a right angle. This makes , by definition, a right triangle.

### Example Question #4 : Angles And Triangles

Which of the following follows from the fact that ?

Explanation:

A congruency statement about two triangles implies nothing about the relationship between two angles of one of the triangles, so  is not correct.

Also, letters in the same position between the two triangles refer to corresponding - and subsequently, congruent - angles. Therefore,  implies that:

Of the given choices, only  is a consequence. It is the correct response.

### Example Question #5 : Angles And Triangles

An exterior angle of an isosceles triangle measures . What is the greatest measure of any of the three angles of the triangle?

Insufficient information is given to answer this question.

Insufficient information is given to answer this question.

Explanation:

The triangle has an exterior angle of , so it has an interior angle of . 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 . The third angle will have measure

.

will be the greatest of the angle measures.

Case 2: One angle has measure  and the others are congruent. Their common measure will be

.

will be the greatest of the angle measures.

The given information is therefore inconclusive.

### Example Question #8 : Angles And Triangles

An exterior angle of an isosceles triangle measures . What is the least measure of any of the three angles of the triangle?

Insufficient information is given to answer this question

Explanation:

The triangle has an exterior angle of , so it has an interior angle of . 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 . The third angle will have measure

.

will be the least of the angle measures.

Case 2: One angle has measure  and the others are congruent. Their common measure will be

.

will be the least of the angle measures.

In both cases, the least of the degree measures of the angles will be .

### Example Question #6 : Angles And Triangles

An exterior angle of an isosceles triangle measures . What is the least measure of any of the three angles of the triangle?

Insufficient information is given to answer this question.

Explanation:

The triangle has an exterior angle of , so it has an interior angle of .

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 -  - each has measure .This is the correct response.

### Example Question #7 : Angles And Triangles

An exterior angle of an isosceles triangle measures . What is the greatest measure of any of the three angles of the triangle?

Insufficient information is given to answer this question.

Explanation:

The triangle has an exterior angle of , so it has an interior angle of .

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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