Common Core Standards: Math
5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
Finding a missing angle is a lot like solving a crime: you've got to sift through all the different clues before you can catch the culprit. And it's high time we transformed your students into geometry detectives.
Luckily, they've got a whole arsenal of tricks to help them in their quest for math-justice.
Supplementary angles are adjacent angles that add up to 180° (i.e., a straight line), whereas complementary angles add up to a right angle (90°). And vertical angles are, of course, straight-up congruent to each other. Armed with all these terms, your students should be able to whip up a nice, simple equation to track down that missing angle.
For example, students should be able to find x by noting that it's supplementary to the 130° angle. So their equation would be 130 + x = 180, or if they're feeling fancy, x = 180 – 130. Once they've found out that x = 50°, they can get even crazier and find y with another equation: 50 + y + 90 = 180. If they're overachievers, they can even find that final missing angle on the bottom: it's a vertical angle to x, so it's also 50°.
While it's important that students use complementary, supplementary, and vertical angles to find these angle measures, it's less important how they find the measures. As long as they're exercising their geometry muscles, we aren't picky.
It's like a detective making a bunch of small deductions, each one building on the previous one. And the way the angles are set up? Those are the clues. Agatha Christie would be proud.