Two pages of visual notes for students to keep: the key words with pictures, how to tell which rule to use, four solved problems in the style of the Laser Heist game, and where these angles show up in real life. To make a PDF, click Print and choose "Save as PDF."
Visual Notes: Angle Relationships
Grades 7–8 · CCSS 7.G.B.5, 8.G.A.5 · Pairs with the Laser Heist: Angle Breaker game
Name
The big idea: when lines cross, their angles come in pairs that are either equal or add up to 90° or 180°. In the Laser Heist, you turn the laser by the angle you find. Spot the pair, decide “equal” or “adds up”, and solve.
Key vocabulary (the colors show the angles each word is about)
Complementary
Two angles that add to 90°.
Supplementary
Two angles that add to 180°.
Vertical angles
Across from each other where two lines cross. Equal.
Parallel lines
Lines in the same plane that never meet; they stay the same distance apart.
Transversal
A line that crosses two or more lines (blue).
Corresponding
Same spot at each crossing. Equal.
Alternate interior
Between the lines, opposite sides. Equal.
Co-interior
Between the lines, same side. Add to 180°.
Which rule do I use? (equal, or add up?)
A little box?Add to 90°
A straight line?Add to 180°
An X?Across: equal
A Z?Alternate interior: equal
An F?Corresponding: equal
A C or U?Co-interior: add to 180°
Shortcut for parallel lines: at two parallel lines cut by a transversal there are only two sizes of angle, a small one and a big one, and small + big = 180°. Every small angle is equal to every other small angle.
x is across from 55°: vertical angles are equal, so x = 55°.
y is next to 55° on a straight line: they add to 180°.
y = 180 − 55 = 125°
✓ Check: 55 + 125 = 180
2. A beam across two parallel walls
∠2 = 72°. Find ∠6 and ∠8.
∠2 and ∠6 are corresponding (an F): equal, so ∠6 = 72°.
∠8 is a big angle (the small ones are 72°): ∠8 = 180 − 72 = 108°.
✓ Check: ∠6 + ∠8 make a straight line: 72 + 108 = 180
3. Co-interior angles with x
∠4 = (2x + 10)° and ∠6 = (x + 20)°.
Between the lines, same side (a C): they add to 180°.
(2x + 10) + (x + 20) = 180, so 3x + 30 = 180
3x = 150, x = 50. ∠4 = 110°, ∠6 = 70°
✓ Check: 110 + 70 = 180
4. Challenge: complementary with x
The box means they add to 90°: x + (3x − 10) = 90
4x − 10 = 90, so 4x = 100
x = 25. The angles: 25° and 3(25) − 10 = 65°
✓ Check: 25 + 65 = 90
Watch out
First decide: equal or add up? Then write the equation. Setting two co-interior angles equal is the most common mistake.
The Z, F and C rules only work when the lines are parallel.
After solving for x, plug it back in: the question usually asks for the angles.
Where you see it in real life
Mirrors: a laser bounces off at the angle it came in.Streets: an avenue is a transversal; the marked corners are equal.Scissors: blades and handles make equal vertical angles.Ladder: its angles with the ground and wall add to 90°.Ramp: its angles with the flat ground add to 180°.