Question

Using the Sum of Exterior Angles

Examine the diagram.



Follow these steps to apply what you have learned about the angles of a triangle.

Find m∠B : 100° + 127° + m∠B = 360°

Then, find the measure of angle A.

Which is the measure of angle A?

133°

53°

47°     

80°

Answer 1

First find m∠B: 100° + 127° + m∠B = 360° → m∠B = 360 − 227 = 133°.

An exterior angle equals the sum of the two remote interior angles, so 133° = m∠A + m∠C. From the diagram m∠C = 80°, therefore m∠A = 133° − 80° = 53°.

Answer: 53°.