Question
\( \angle A B C \) 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. \( 150^{\circ} \)
Ask by Floyd Medina. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \angle ABD = 50^\circ \).
Solution
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. \( 50^{\circ} \)**
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Simplify this solution Extra Insights
When a ray bisects an angle, it divides the angle into two equal parts. Since \( \angle A B C = 100^{\circ} \) and ray \( B D \) bisects it, we can find \( \mathrm{m} \angle A B D \) by dividing \( 100^{\circ} \) by 2. So, \( \mathrm{m} \angle A B D = \frac{100^{\circ}}{2} = 50^{\circ} \). The answer is B. \( 50^{\circ} \).
