Question

1. in △abc, d is on ac, and bd is a bisector of ∠abc. what is the measure of ∠dbc? m∠dbc =

Explanation:

Step1: Find the measure of ∠ABC

Use the triangle - angle - sum theorem. In △ABC, ∠A + ∠B+∠C = 180°. Given ∠A = 36° and ∠C = 75°.
So, ∠ABC=180°-(∠A + ∠C)=180°-(36° + 75°)=180° - 111° = 69°.

Step2: Use the angle - bisector definition

Since BD is the bisector of ∠ABC, then ∠DBC=\(\frac{1}{2}\)∠ABC.
Substitute ∠ABC = 69° into the formula. So, ∠DBC=\(\frac{69°}{2}=34.5°\).

Answer:

34.5°