\( \angle A B C \) is bisected by ray \( B D . \mathrm{m} \angle A B C=100^{\circ} \). What is \( \mathrm{m} \angle A B D \) ? A. \( 75^{\circ} \) B. \( 50^{\circ} \) C. \( 100^{\circ} \) D. \( 150^{\circ} \)

To determine the measure of angle \( \angle ABD \) when ray \( BD \) bisects \( \angle ABC \), follow these steps: 1. **Given Information:** - \( \angle ABC = 100^\circ \). - Ray \( BD \) bisects \( \angle ABC \). 2. **Understanding the Bisector:** - A bisector divides an angle into two equal parts. - Therefore, \( \angle ABD = \angle DBC \). 3. **Calculate the Measure of Each Smaller Angle:** \[ \angle ABD = \frac{\angle ABC}{2} = \frac{100^\circ}{2} = 50^\circ \] **Answer:** **B. \( 50^{\circ} \)**