In triangle $△abc$, which angle's measure is equal to the sum of the measures of $\angle bac$ and $\angle bca$?

• A. $\angle bcf$
• B. $\angle cbe$
• C. $\angle cba$
• D. $\angle dac$

Answer: (A)

Verified step by step guidance

1. Recall the Triangle Angle Sum Theorem, which states that the sum of the interior angles of any triangle is \$180^\circ$.
2. Identify the angles given: \(\angle b a c\) and \(\angle b c a\). These are two angles in triangle \(\triangle a b c\) sharing vertex points \(a\) and \(c\) respectively.
3. Understand that the third angle in the triangle, \(\angle c a b\), must be equal to the sum of the other two angles subtracted from \$180^\circ$.
4. Since the problem asks which angle's measure equals the sum of \(\angle b a c\) and \(\angle b c a\), consider the exterior angle theorem: an exterior angle of a triangle equals the sum of the two opposite interior angles.
5. Therefore, the angle that equals the sum of \(\angle b a c\) and \(\angle b c a\) is the exterior angle at vertex \(b\), which is \(\angle c b a\).