Question

The angle ∡ABC = 40, BD is the bisector of ∡ABC, BE is the ∡CBD bisector of What is the measure of ∡ABE 10 60 20 30 None of them 15

Answer 1

The measure of angle ABE is 30 degrees.

Step-by-step explanation:

The measure of angle ABE can be found by applying the Angle Bisector Theorem. In this case, BD is the bisector of angle ABC and BE is the bisector of angle CBD. According to the theorem, the ratio of the lengths of the segments formed by the angle bisector is equal to the ratio of the lengths of the opposite sides of the angle. So, we can set up the following equation:

(AE / CE) = (AB / BC)

Since the measure of angle ABC is given as 40 degrees, the ratio of the lengths of AB to BC is 1, because AB and BC are congruent sides of an isosceles triangle. Therefore, we can substitute AB = BC and simplify the equation to:

(AE / CE) = 1

This means that AE is equal in length to CE. Since an angle and its bisector divide a convex angle into two congruent angles, we can conclude that angle ABE is congruent to angle CBE. Therefore, the measure of angle ABE is equal to the measure of angle CBE, which is half of angle CBD. Since angle CBD is given as 60 degrees, angle ABE is:

∡ABE = ∡CBE = 1/2 ∡CBD = 1/2 * 60 = 30 degrees

Learn more about Angle Bisector Theorem