Question

unit #1 - lesson #7 exit ticket: in the diagram below, $overline{ab}$ is perpendicular to $overline{bc}$ and $overline{be}$ bisects $angle dbc$. if the measure of $angle abd$ is $20^{circ}$ then find the measure of $angle dbe$. justify your answer. answer:

Explanation:

Step1: Determine the measure of ∠DBC

Since AB is perpendicular to BC, ∠ABC = 90°. Given ∠ABD=20°, then ∠DBC=∠ABC - ∠ABD. So, ∠DBC = 90° - 20°=70°.

Step2: Use the angle - bisector property

Since BE bisects ∠DBC, by the definition of an angle - bisector, ∠DBE=\frac{1}{2}∠DBC. Substitute ∠DBC = 70° into the formula, we get ∠DBE=\frac{70^{\circ}}{2}=35°.

Answer:

35°