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 ∠B in △ABC

Sum of angles in 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 △ABC: $\angle A=50^\circ$, $\angle B=88^\circ$, $\angle ACB=42^\circ$
In △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:

△ABC is similar to △DEC.