The sum of the measures of the
angles of a trapezoid is 360 degrees. Write an equation to find the
missing measure 𝑥, and then solve it.
We’re given information about the
sum of the interior angles. But of course, a trapezoid is a
four-sided polygon; it’s a quadrilateral. So we actually know that the
interior angles sum to make 360 degrees. Let’s use this information to write
an equation. We’re going to begin by adding
together the measure of each of our angles. That’s 𝑥 plus 102 plus 116 plus
78. We, of course, know that the sum
total of these four angles has to be 360 degrees. So our equation is 𝑥 plus 102 plus
116 plus 78 equals 360.
We need to solve this to find the
value of 𝑥. So let’s begin by simplifying the
left-hand side. 102 plus 116 plus 78 is 296. So our equation becomes 𝑥 plus 296
equals 360. To solve, we perform the inverse
operations. Well, at the moment, we’re adding
296. So the inverse, the opposite to
that, is to subtract 296. 𝑥 plus 296 minus 296 is just
𝑥. And 360 minus 296 is 64. So the missing measure 𝑥, our
fourth angle at 𝐷, is 64 or 64 degrees.