Question

Triangle A B C is shown with its exterior angles. Line B A extends through point D. Line A B extends through point E. Line A C extends through point F.
Which angle’s measure is equal to the sum of the measures of ∠BAC and ∠BCA?

∠CBA
∠CBE
∠DAC
∠BCF

Answer 1

∠CBE

Reason: ∠CBE is the exterior angle at vertex B (since AB is extended through B to E). By the exterior-angle theorem, an exterior angle equals the sum of the two remote interior angles, here ∠BAC and ∠BCA.