Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 6 - Polygons and Quadrilaterals - Mid-Chapter Quiz - Page 398: 2


$m = 116$ $a = 105$

Work Step by Step

We can find $m$ because $m$ and its adjacent angle are supplementary angles. We can set up an equation using this information: $m = 180 - 64$ Subtract to solve for $m$: $m = 116$ We can now find $a$ because we have the measures of all the interior angles except for $a$. We can use a formula to find $w$ based on the measurement of the interior angles. First, we find the sum of the interior angles: sum of interior angles = $(n - 2)(180)$ We have four sides, so $n = 4$. Let's plug this into the formula: sum of interior angles = $(4 - 2)(180)$ Evaluate parentheses first: sum of interior angles = $2(180)$ Multiply to solve: sum of interior angles = $360$ $360 = 50 + 89 + 116 + a$ Add terms on the right side of the equation: $360 = 255 + a$ Subtract $255$ from each side of the equation to solve for $a$: $a = 105$
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