Question

1. if $\triangle xyzcong\triangle pqr$ and $angle x = 40^{circ}$, what is the measure of $angle p$?

a. $50^{circ}$
b. $90^{circ}$
c. $30^{circ}$
d. $40^{circ}$

Explanation:

Step1: Use the property of congruent triangles

When \(\triangle XYZ\cong\triangle PQR\), corresponding angles are equal. That is \(\angle X=\angle P\), \(\angle Y = \angle Q\), \(\angle Z=\angle R\).

Step2: Substitute the given value

Given \(\angle X = 40^{\circ}\), since \(\angle X=\angle P\) (corresponding angles of congruent triangles \(\triangle XYZ\) and \(\triangle PQR\)), then \(\angle P=40^{\circ}\).

Answer:

d. \(40^{\circ}\)