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

Question

Accepted Answer

# Explanation:
## Step1: Find angle $ B $ in $ \triangle ABC $
Use the triangle - angle sum theorem ($ \angle A+\angle B+\angle ACB = 180^{\circ} $). Given $ \angle A = 50^{\circ} $ and $ \angle ACB=42^{\circ} $.
$$
\begin{align*}
\angle B&=180^{\circ}-\angle A - \angle ACB\
&=180^{\circ}-50^{\circ}-42^{\circ}\
&=88^{\circ}
\end{align*}
$$
## Step2: Find angle $ D $ in $ \triangle DEC $
Use the triangle - angle sum theorem ($ \angle D+\angle E+\angle DCE = 180^{\circ} $). Since $ \angle DCE=\angle ACB = 42^{\circ} $ (vertical angles) and $ \angle E = 88^{\circ} $.
$$
\begin{align*}
\angle D&=180^{\circ}-\angle E-\angle DCE\
&=180^{\circ}-88^{\circ}-42^{\circ}\
&=50^{\circ}
\end{align*}
$$
## Step3: Check for similarity
In $ \triangle ABC $ and $ \triangle DEC $, $ \angle A=\angle D = 50^{\circ} $, $ \angle B=\angle E = 88^{\circ} $, and $ \angle ACB=\angle DCE = 42^{\circ} $. By the AA (angle - angle) similarity criterion ($ \triangle ABC\sim\triangle DEC $ since two pairs of corresponding angles are equal).

# Answer:
$\triangle ABC$ is similar to $\triangle DEC$.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Find angle \( B \) in \( \triangle ABC \)

Step2: Find angle \( D \) in \( \triangle DEC \)

Step3: Check for similarity

Answer: