Question

in exercises 35-38, bd bisects labc. find m /abd, ma) m /abd = 45°, mb) m /abd = 60°, mc) m /abd = 30°, md) m /abd = 75°, m

Answer 1

To find the measure of angle ABC given that BD bisects angle ABC, one must double the measure of angle ABD given in each case, resulting in 90°, 120°, 60°, and 150° respectively.

Step-by-step explanation:

The question asks us to find the measure of angle ABD when BD bisects angle ABC and the measures of angle ABD are given (45°, 60°, 30°, and 75° respectively). When a line bisects an angle, it divides the angle into two equal parts. Therefore, to find the measure of angle ABC in each case, we simply double the measure of angle ABD. Here are the solutions:

• ma) m∖ABC = 2 * m∖ABD = 2 * 45° = 90°
• mb) m∖ABC = 2 * m∖ABD = 2 * 60° = 120°
• mc) m∖ABC = 2 * m∖ABD = 2 * 30° = 60°
• md) m∖ABC = 2 * m∖ABD = 2 * 75° = 150°