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\\)? \\(\boldsymbol{a}\\) \\(70^\circ\\) \\(\boldsymbol{b}\\) \\(68^\circ\\) \\(\boldsymbol{c}\\) \\(41^\circ\\) \\(\boldsymbol{d}\\) \\(22^\circ\\)

Explanation:

Step1: Recall Similar Triangles Property

In similar triangles, corresponding angles are equal. So, the order of the letters in the triangle names (ΔABC ~ ΔXYZ) tells us the corresponding angles. That means ∠A corresponds to ∠X, ∠B corresponds to ∠Y, and ∠C corresponds to ∠Z.

Step2: Determine Measure of ∠Y

Since ∠B corresponds to ∠Y and the measure of ∠B is \( 68^\circ \), the measure of ∠Y must also be \( 68^\circ \) because corresponding angles in similar triangles are equal.

Answer:

B. \( 68^\circ \)