Video: Writing and Solving Linear Equations to Find the Missing Angle’s Measure in a Quadrilateral

The sum of the measures of the angles of a trapezoid is 360°. Write an equation to find the missing measure 𝑥, and then solve it.

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Video Transcript

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.

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