Question

△abc and △dec are shown below. which statement is true? △abc is similar to △dec. △abc is not similar to △dec. there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Calculate $\angle B$ in $\triangle ABC$

Sum of angles in a triangle is $180^\circ$.
$\angle B = 180^\circ - 50^\circ - 42^\circ = 88^\circ$

Step2: Identify vertical angles

$\angle ACB$ and $\angle DCE$ are vertical angles, so $\angle ACB = \angle DCE = 42^\circ$

Step3: Match corresponding angles

In $\triangle ABC$: $\angle A=50^\circ$, $\angle B=88^\circ$, $\angle ACB=42^\circ$
In $\triangle DEC$: $\angle E=88^\circ$, $\angle DCE=42^\circ$, so $\angle D=180^\circ-88^\circ-42^\circ=50^\circ$
All corresponding angles are equal.

Answer:

$\triangle ABC$ is similar to $\triangle DEC$.