Questions: BIG IDEAS MATH Geometry: CC 2015 Chapter 5: Congruent Polygons Section Exercises 5.2 Exercise 7 In the figure, triangle XYZ is congruent to triangle MNL. Find m angle Z. m angle Z =

BIG IDEAS MATH Geometry: CC 2015 Chapter 5: Congruent Polygons Section Exercises 5.2 Exercise 7

In the figure, triangle XYZ is congruent to triangle MNL. Find m angle Z.

m angle Z =

Transcript text: BIG IDEAS MATH Geometry: CC $2015>$ Chapter 5: Congruent Polygons > Section Exercises $5.2>$ Exercise 7 In the figure, $\triangle XYZ \cong \triangle MNL$. Find $m \angle Z$. $m \angle Z=\square$

Solution

Solution Steps

Step 1: Find the measure of angle Y.

The sum of the angles in a triangle is 180°. In triangle XYZ, we are given angle X is 33°. We know triangle XYZ is congruent to triangle MNL. Since corresponding angles of congruent triangles are congruent, angle Y is congruent to angle N which is 124°. Therefore m∠Y = 124°.

Step 2: Find the measure of angle Z.

The sum of the angles in triangle XYZ is 180°. m∠X + m∠Y + m∠Z = 180° 33° + 124° + m∠Z = 180° 157° + m∠Z = 180° m∠Z = 180° - 157° m∠Z = 23°