Triangle angle problem

Geometry Level 3

Triangle $ABC$ is isosceles with $\angle B=\angle C=40^{\circ}$ and $BC=10$ . Extend $AB$ to point $D$ so that $AD=10$ . Find $\angle ACD$ .

The answer is 50.

1 solution

Julian Yu
Nov 26, 2018

Let $E$ be a point such that $\triangle ADE$ is equilateral (A and E are on opposite sides of BC). Triangles $ABC, ACE$ are congruent since $AB=AC, BC=AD=AE, \angle ABC=\angle CAE=40^\circ.$

Thus $AC=CE$ and $ADEC$ is a kite, so $DC \bot AE \Leftrightarrow \boxed{\angle ACD=50^\circ}$

Triangle angle problem

The answer is 50.

1 solution

0 pending reports