Answer
$m = 116$
$a = 105$
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 $a$:
$a = 105$
