### All GED Math Resources

## Example Questions

### 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:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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 #4 : Angles And Triangles

Figure drawn to scale.

Refer to the above diagram.

Which of the following is a valid description of ?

**Possible Answers:**

Equiangular

Right

Obtuse

Acute

**Correct answer:**

Obtuse

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 #5 : Angles And Triangles

Refer to the above diagram.

Which of the following is a valid description of ?

**Possible Answers:**

Equiangular

Acute

Obtuse

Right

**Correct answer:**

Right

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

### Example Question #5 : Angles And Triangles

Which of the following follows from the fact that ?

**Possible Answers:**

**Correct answer:**

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 #6 : 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?

**Possible Answers:**

Insufficient information is given to answer this question.

**Correct answer:**

Insufficient information is given to answer this question.

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 #7 : 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?

**Possible Answers:**

Insufficient information is given to answer this question

**Correct answer:**

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 #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?

**Possible Answers:**

Insufficient information is given to answer this question.

**Correct answer:**

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 #9 : 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?

**Possible Answers:**

Insufficient information is given to answer this question.

**Correct answer:**

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.