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# Common Core Standards: Math

#### The Standards

# Grade 7

### Geometry 7.G.B.5

**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.