Questions: If triangle ABC is congruent to triangle DEC, angle ABC = 2x, angle BCA = 48°, and angle CDE = 74°

Transcript text: If $\triangle A B C \cong \triangle D E C, \angle A B C=2 x$, $\angle B C A=48^{\circ}$, and $\angle C D E=74^{\circ}$

Solution

Solution Steps

Step 1: Find the measure of

\angle ACB

Since the sum of the angles in $\triangle ABC$ is $180^\circ$ , we have $\angle CAB + \angle ABC + \angle BCA = 180^\circ$ . Substituting the given values, we get $\angle CAB + 2x + 48 = 180$ , so $\angle CAB = 132 - 2x$ .

Step 2: Use the congruent triangles.

Since $\triangle ABC \cong \triangle DEC$ , we have corresponding angles congruent. Therefore, $\angle ABC \cong \angle DEC$ , so $2x = \angle DEC$ . Also, $\angle BCA \cong \angle ECD$ , so $48^\circ = \angle ECD$ . And, $\angle CAB \cong \angle CDE$ , so $132 - 2x = 74$ .