Question Video: Finding the Measure of Two Angles by the Supplementary and Complementary Angles' Rule Mathematics

Determine the values of 𝑥 and 𝑦.

02:06

Video Transcript

Determine the values of 𝑥 and 𝑦.

We begin by noticing that the two angles with measures 62 degrees and 𝑥 degrees form a right angle. This means that they are complementary angles as complementary angles sum to 90 degrees. We can write this as an equation. 𝑥 degrees plus 62 degrees is equal to 90 degrees. And since all the angles have the same unit, 𝑥 plus 62 is equal to 90. We can then subtract 62 from both sides of the equation. And this means that 𝑥 is equal to 28.

In order to determine the value of 𝑦, we note that all four angles lie on a straight line. The angle of measure 𝑦 degrees combines with the angle that is the sum of 𝑥 degrees, 62 degrees, and 37 degrees to make a straight angle. In other words, these angles are supplementary since supplementary angles sum to 180 degrees. We have the equation 𝑦 degrees plus 𝑥 degrees plus 62 degrees plus 37 degrees is equal to 180 degrees. And since 𝑥 is equal to 28, this simplifies as shown. Adding 28, 62, and 37 gives us 127. So our equation becomes 𝑦 plus 127 is equal to 180. We can then subtract 127 from both sides, giving us 𝑦 is equal to 53. The values of 𝑥 and 𝑦 are 28 and 53, respectively.

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