We are given a circle with center at the dot. We are given $m\angle BDC = 38^\circ$, and the $m\angle BCD = 70^\circ$. We want to find the measure of the arc $BC$.

1. Problem Description

We are given a circle with center at the dot. We are given $m\angle BDC = 38^\circ$, and the $m\angle BCD = 70^\circ$. We want to find the measure of the arc $BC$.

2. Solution Steps

The measure of an inscribed angle is half the measure of its intercepted arc.

In this case, $\angle BDC$ is an inscribed angle that intercepts arc $BC$. Therefore, the measure of arc $BC$ is twice the measure of $\angle BDC$.

$$m(\text{arc }BC) = 2 \cdot m\angle BDC$$

$$m(\text{arc }BC) = 2 \cdot 38^\circ$$

$$m(\text{arc }BC) = 76^\circ$$

3. Final Answer

$76$