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

Example Questions

Example Question #6 : Acute / Obtuse Triangles

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

Explanation:

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

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

In a given triangle, the angles are in a ratio of 1:3:5.  What size is the middle angle?

Explanation:

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 #2 : 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

41

98

90

82

98

Explanation:

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 #2 : How To Find An Angle In An Acute / Obtuse Triangle

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

50°

80°

60°

70°

50°

Explanation:

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 #61 : Triangles

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 .