Question

triangle abc, shown in the diagram below, is an isosceles triangle. if the measure of ∠acd is 130°, what is the measure of ∠abc? 220° 50° 65° 130°

Explanation:

Step1: Find the measure of ∠ACB

Since ∠ACD and ∠ACB are supplementary (a straight - line angle is 180°), we have ∠ACB=180° - ∠ACD.
∠ACB = 180°-130°=50°.

Step2: Use the property of isosceles triangle

In isosceles triangle ABC, AC = AB, so ∠ABC=∠ACB.
Since ∠ACB = 50°, then ∠ABC = 50°.

Answer:

50°