Question

consider that $\triangle abc$ is similar to $\triangle xyz$ and the measure of $\angle b$ is $68^\circ$. what is the measure of $\angle y$? a $70^\circ$ b $68^\circ$ c $41^\circ$ d $22^\circ$

Explanation:

Step1: Recall properties of similar triangles

Similar triangles have corresponding angles equal. So, in similar triangles \( \triangle ABC \) and \( \triangle XYZ \), the corresponding angles are congruent.

Step2: Identify corresponding angles

Since \( \triangle ABC \sim \triangle XYZ \), the order of the letters implies that \( \angle B \) corresponds to \( \angle Y \).

Step3: Determine the measure of \( \angle Y \)

Given \( m\angle B = 68^\circ \), and because corresponding angles in similar triangles are equal, \( m\angle Y = m\angle B = 68^\circ \).

Answer:

B. \( 68^\circ \)