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Geometry and Measurement 6-8 / Week 08 / Monday
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Week 08 · Angles

Monday

Angles in pairs
// Pairs that add up, pairs that match
⏱ about 20 min

Monday: Angles in Pairs

Rocket leans a straw against the roof beam on the Blueprint Table. "The roof slope. I measured it: 40 degrees."

"Then what is the angle on the other side of the straw?" Raven asks. "Where it meets the beam."

Rocket sets the protractor down. "Why measure? I will just read it." He squints. "About 140."

"What do you notice about 40 and 140?" Raven asks.

"They make 180," Rocket says. "A straight line. So I never needed to measure the second one."

Nova hovers above the beam, her light splitting at the straw. "One angle known, one angle found," she says. "That is this week."

Rocket is already drawing crossing lines. Nova hums. "Four angles at a crossing. Measure one, know them all."

Rocket holds a protractor on a straw roof triangle while Raven lays two parallel sticks crossed by a third, Nova above.

Four kinds of pairs

PairRulePicture in words
supplementaryadd to 180°two angles along a straight line
complementaryadd to 90°two angles that fill a square corner
verticalequalthe angles opposite each other where two lines cross
adjacentadd to the whole angletwo angles side by side, sharing one ray
Two angles along a straight line: 40° and a second angle marked with a question mark

The straw makes 40° with the beam on one side. The other side is the rest of the straight line: 40 + ? = 180, so ? = 140°.

That is the whole method. Name the pair, write its rule as an equation, and solve.

Two crossing lines with one angle of 110° and the opposite angle marked with a question mark

Where two lines cross, the opposite angles are vertical angles and they match. If one is 110°, the one across from it is 110° too.

The two angles next to it are supplementary with 110: each is 70°. Measure one angle and you know all four.

NAME THE PAIR
  • Read the question.
  • Tap your answer.
Two angles side by side measure 40° and 140°. What kind of pair are they?
Two angles side by side measure 35° and 55°. What kind of pair are they?
Two lines cross. The angles opposite each other are both 110°. What kind of pair are they?
Two angles side by side measure 25° and 45°. What kind of pair are they?
FIND THE MISSING ANGLE
  • Read the question.
  • Tap your answer.
Two angles side by side making 180°; one is 40° and the other is marked ?The two angles are supplementary. One is 40°. What is the other, in degrees?
Two angles side by side making 90°; one is 35° and the other is marked ?The two angles are complementary. One is 35°. What is the other, in degrees?
Two crossing lines; one angle is 110° and the angle opposite it is marked ?The two angles are vertical. One is 110°. What is the other, in degrees?
Two angles side by side making 70°; one is 25° and the other is marked ?The two angles are adjacent and make 70° together. One is 25°. What is the other, in degrees?
The roof straw makes 40° with the beam. What is the other angle along the beam, in degrees? Type the number.
WHY THIS EXERCISESupplementary angles let you find a second angle without picking up the protractor again.
Try it
Lay two straws so they cross on the table. Measure one of the four angles with a protractor.
Predict the other three using the pair rules. Then measure to check.
Safety first
Straws and sticks stay on the table. No one runs with a straw or points one at a face.
The protractor is plastic. Keep it flat on the paper and read it from above.
Draw two crossing lines. Write 110° in one angle, then fill the other three using the pair rules.

Pairs with rules. Tomorrow you write the rules as equations and solve for angles you cannot see.