Question

Interpreting Statements about Angles in a Triangle
Examine the diagram. It is not drawn to scale.

A triangle has angles A, B, 80 degrees. The exterior angle to angle A is 150 degrees.

Choose the statements that are true based on the diagram.
∠A is supplementary to the exterior angle.
∠A and the 80° angle are remote interior angles.
80° + m∠B + 150° = 360°.
∠B measures 70°.
∠A measures 40°.

Answer 1

True:
- ∠A is supplementary to the exterior angle. (They form a linear pair, so A + 150° = 180°.)
- ∠B measures 70°. (Exterior ∠ = sum of the two remote interior angles, so 150° = 80° + m∠B ⇒ m∠B = 70°.)

False:
- ∠A and the 80° angle are remote interior angles. (For the exterior at A, the remote interior angles are ∠B and 80°, not ∠A.)
- 80° + m∠B + 150° = 360°. (With m∠B = 70°, this sum is 300°, not 360°.)
- ∠A measures 40°. (From A + 150° = 180°, m∠A = 30°.)