### All ACT Math Resources

## Example Questions

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

Two interior angles in an obtuse triangle measure and . What is the measurement of the third angle.

**Possible Answers:**

**Correct answer:**

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

### Example Question #2 : 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:**

**Correct answer:**

Since the sum of the angles of a triangle is , 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:

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.

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

In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?

A (Angle A = 41°)

B C

**Possible Answers:**

98

41

82

90

**Correct answer:**

98

If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:

41° + 41° = 82°

Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:

180° - 82° = 98°

### Example Question #4 : Acute / Obtuse Triangles

Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.

**Possible Answers:**

50°

80°

60°

70°

**Correct answer:**

50°

To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.

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

Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is . The measure of angle CBD is . The length of segment is 4.

Find the measure of .

**Possible Answers:**

**Correct answer:**

The measure of is . Since , , and are collinear, and the measure of is , we know that the measure of is .

Because the measures of the three angles in a triangle must add up to , and two of the angles in triangle are and , the third angle, , is .