Question

question 4
triangle abc, shown in the diagram below, is an isosceles triangle.
if the measure of ∠acd is 130°, what is the measure of ∠abc?
130°
50°
65°
220°

Explanation:

Step1: Find adjacent - interior angle

$\angle ACB=180^{\circ}-\angle ACD = 180 - 130=50^{\circ}$

Step2: Use isosceles - triangle property

In $\triangle ABC$, since $AC = AB$, $\angle ABC=\angle ACB$. So $\angle ABC = 65^{\circ}$ (because $\triangle ABC$ is isosceles and the base - angles are equal).

Answer:

C. $65^{\circ}$