Which angle’s measure is equal to the sum of the meaures of ∠bac and ∠bca? ∠cba ∠cbe ∠dac ∠bcf

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 389 People

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

Answered by maham237 @ 25/12/2020

Answer:

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

Step-by-step 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

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