## Elementary Geometry for College Students (7th Edition)

Published by Cengage

# Chapter 4 - Review Exercises - Page 217: 16

#### Answer

$\angle M = 100˚$ $\angle P = 80˚$

#### Work Step by Step

This is a parallelogram so therefore a property for this shape is congruent angles, meaning that the opposite angles are equal to each other. 1. Solve for $x$ using the formula: $\angle M = \angle O$ (congruent angles) $\angle M = \angle O$ $4x = 2x + 50$ $2x = 50$ $x = 25$ 2. Solve for $\angle M$ by substituting the $x$ value into the $\angle M$ formula $\angle M = 4x$ $\angle M = 4(25)$ $\angle M = 100˚$ 3. Substitute $x$ into the $\angle O$ formula and then apply the concept of congruent angles to find $\angle P$ $\angle P = (180) - (2x + 50)$ $\angle P = (180) - (2(25) + 50)$ $\angle P = (180) - (50 + 50)$ $\angle P = 180 - 100$ $\angle P = 80˚$

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