Two pages of visual notes for students to keep: the key words with pictures, how to tell complementary from supplementary, four solved problems in the style of the Bank Shot game, and where these angles show up in real life. To make a PDF, click Print and choose "Save as PDF."
Visual Notes: Complementary and Supplementary Angles
Grade 7 · CCSS 7.G.B.5 · Pairs with the Bank Shot: Angle Golf game
Name
The big idea: some pairs of angles always add up to the same total. If they make a corner (a right angle) they add to 90°. If they make a straight line they add to 180°. Know one angle, subtract, and you have the other. In Bank Shot, that's how you aim the ball off the walls.
Key vocabulary (the colors show the angles each word is about)
Angle
Two rays that share an endpoint (the vertex). Its size is how far one ray turns from the other.
Degree (°)
The unit for measuring angles. A full turn is 360°, so each of 8 equal pizza slices is 45°.
Right angle
Exactly 90°, a square corner. It's marked with a little box.
Straight angle
Exactly 180°. Its two sides make a straight line.
Complementary angles
Two angles that add to 90°: 35° + 55° = 90°.
Supplementary angles
Two angles that add to 180°: 70° + 110° = 180°.
Which rule do I use? (look at the picture first)
A corner (little box)?Complementary: 90 − the angle you know
A straight line?Supplementary: 180 − the angle you know
Two lines make an X?The angles across from each other (vertical angles) are equal.
Memory trick:C comes before S in the alphabet, and 90 comes before 180. Complementary makes a Corner; Supplementary makes a Straight line.
Visual Notes: Complementary and Supplementary Angles, page 2
1. Find the complement
Spot it: the little box means the two angles make 90°.
Write it: x + 28 = 90
Solve it: x = 90 − 28 = 62°
✓ Check: 62 + 28 = 90
2. Find the supplement
Spot it: the two angles sit on a straight line, so they make 180°.
Write it: x + 135 = 180
Solve it: x = 180 − 135 = 45°
✓ Check: 45 + 135 = 180
3. A missing angle with an expression
Straight line, so: (2x + 10) + 50 = 180
Combine: 2x + 60 = 180
Subtract 60: 2x = 120. Divide by 2: x = 60
The angle: 2(60) + 10 = 130°
✓ Check: 130 + 50 = 180
4. Challenge: an angle is twice its complement
Call the complement x. The angle is 2x.
Together they make 90°: x + 2x = 90
3x = 90, so x = 30
The angles: 30° and 60°
✓ Check: 60 is twice 30, and 30 + 60 = 90
Watch out
Complementary means 90°, supplementary means 180°. Mixing them up is the most common mistake.
An angle bigger than 90° has no complement. An angle of 180° or more has no supplement.
When the angle is an expression, solve for x, then plug x back in to find the angle.
Where you see it in real life
Mini golf: a ball banks off a wall at the angle it came in.Clocks: at 3:00 the hands make a right angle.Ladder: its angles with the ground and wall add to 90°.Ramp: its angles with the flat ground add to 180°.Pizza: equal slices split 360° evenly.