## Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole

# Chapter 4 - Review Exercises: 14

#### Answer

$\angle C = 106˚$

#### Work Step by Step

Since $\square ABCD$ is a parallelogram, this means that $DA$ and $BC$ are parallel to each other and therefore $\angle A + \angle B = 180˚$ $\angle A = 2x + 6$ $\angle B = x + 24$ 1. Solve for $x$ using the formula: $\angle A + \angle B = 180˚$ $(2x+6) + (x+24) = 180˚$ $3x + 30 = 180$ $3x = 150$ $x = 50$ 2. Apply the one of the properties of quadrilaterals, congruent angles. This property specifically states that opposite angles are equal to each other in a parallelogram. Therefore $\angle A = \angle C$ and now we have to solve for $\angle A$. Substitute the $x$ into the $\angle A$ equation. $\angle A = \angle C = (2x+6)$ $\angle A = \angle C = 2(50)+6$ $\angle A = \angle C = 100+6$ $\angle A = \angle C = 106˚$

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