Question

angle bac measures 56°. what is the measure of angle bdc? 28° 34° 56° 112°

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of the intercepted arc. Angles $\angle BAC$ and $\angle BDC$ intercept the same arc $\overset{\frown}{BC}$.

Step2: Apply the theorem

Since $\angle BAC = 56^{\circ}$ and $\angle BDC$ intercepts the same arc as $\angle BAC$, then $m\angle BDC=m\angle BAC$.

Answer:

$56^{\circ}$