Question

Which angle’s measure is equal to the sum of the meaures of ∠BAC and ∠BCA?

∠CBA
∠CBE
∠DAC
∠BCF

Answer 1

sum of interior angle is equal to opposite exterior angles

{ Exterior angle theorem }

answer is < CBE

Answer 2

∠CBE is the angle which is equal to the sum of the measures of ∠BAC and ∠BCA.

Explanation:

Given two angles ∠BAC and ∠BCA in ΔABC

we have to choose the angle which is equal to the sum of the measure of ∠BAC and ∠BCA.

An exterior angle of a triangle forms a linear pair with the adjacent interior angle. The two non-adjacent interior angles to the exterior angle are its remote interior angles

As shown in attachment, ∠CBE is the only angle which is the exterior angle to remote interior angles.

By exterior angle theorem

The measure of the exterior angle of a triangle is equal to the sum of the measure sf its interior angles.

⇒ ∠CBE = ∠BAC + ∠BCA

Hence, ∠CBE is the angle which is equal to the sum of the measures of ∠BAC and ∠BCA.

∴ Option B is correct