Question

What is m∠ABC?

m∠ABC = 15°
m∠ABC = 45°
m∠ABC = 60°
m∠ABC = 75°

Triangle A B C is shown with its exterior angles. Line C B extends through point D. Line B C extends to form exterior angle that is 135 degrees. Angle C A B is 75 degrees.

Answer 1

m∠ABC = 45°.

Reason: The exterior angle at B is 135°, and an exterior angle equals the sum of the two remote interior angles, so ∠A + ∠C = 135°. With ∠A = 75°, ∠C = 135° − 75° = 60°. Then ∠B = 180° − (∠A + ∠C) = 180° − (75° + 60°) = 45°.