Question

which angle’s measure is equal to the sum of the measures of ∠bac and ∠bca?
○ ∠cba
○ ∠cbe
○ ∠dac
○ ∠bcf

Explanation:

Step1: Use triangle angle sum property

In $\triangle ABC$, $\angle BAC + \angle BCA + \angle CBA = 180^\circ$. So $\angle BAC + \angle BCA = 180^\circ - \angle CBA$.

Step2: Check linear pair for $\angle CBE$

$\angle CBA + \angle CBE = 180^\circ$ (linear pair). Thus $\angle CBE = 180^\circ - \angle CBA$.

Step3: Equate the two results

$\angle BAC + \angle BCA = \angle CBE$.

Answer:

B. $\angle CBE$