Friday
Friday: Angles All Around
Rocket opens the scissors on the Blueprint Table. "Two blades crossing. Vertical angles. The handles match the blades."
"The door and the floor," Raven says. "Open it partway: one angle on each side, and they make 180."
"Shelves and their brackets make square corners," Rocket says. "Complementary pairs if a brace cuts across."
"And rafters," Raven says, pointing at the roof frame. "Parallel rafters, one brace. What do you notice?"
"Two sizes of angle, eight places," Rocket says. "I only measure once now."
Nova hovers over the frame, her light ticking from corner to corner. "Review," she says. "Then next week every shape starts moving."
Rocket is already sliding a cardboard L across the table. Nova hums. "Not yet."
Angle pairs in everyday places
| Where | Pair | Rule |
|---|---|---|
| open scissors | vertical | the two blade angles are equal |
| a door standing partway open | supplementary | the two angles with the wall add to 180° |
| a brace across a square shelf corner | complementary | the two angles add to 90° |
| parallel rafters with one brace | corresponding | matching angles at each rafter are equal |
| a triangle sign | angle sum | the three angles add to 180° |
Every angle fact this week came from one idea: a straight line is 180°. Pairs along a line add to it, a triangle's corners fill it, and an exterior angle finishes it.
The week in five lines
- Supplementary: 180. Complementary: 90. Vertical: equal. Adjacent: they add to the whole angle.
- Write the rule as an equation with x, solve, then check the sum.
- The three angles of a triangle add to 180°. The torn corners prove it.
- An exterior angle equals the two far angles added.
- Parallel lines and a transversal make two sizes of angle. Corresponding angles are equal.
- Read the question.
- Tap your answer.
Open scissors make a 35° angle between the blades. What is the angle between the handles, in degrees?
A door stands open at 72° from the wall. What is the angle on the other side of the door, in degrees?
A brace crosses a square shelf corner, making a 28° angle with the shelf. What angle does it make with the upright, in degrees?
Two parallel rafters are crossed by a brace. Angle a at the first rafter is 55°. What is angle e at the second rafter, in degrees?- Read the question.
- Tap your answer.
A triangle has angles of 35° and 65°. What is the third angle, in degrees?
A triangle has angles of 40° and 75°. What is the exterior angle at the third corner, in degrees?| Week review | True or false? |
|---|---|
| Vertical angles are always equal. | ? |
| Complementary angles add to 180°. | ? |
| 35 + 65 + 80 = 180 | ? |
| An exterior angle of a triangle is bigger than either far angle. | ? |
| A transversal across parallel lines makes eight different angle sizes. | ? |
- ?We crossed two parallel sticks with a brace and found two sizes of angle, plus the exterior angle.
- ?We wrote equations with x for unknown angles and solved them.
- ?We named four kinds of angle pairs and found a missing angle from one measurement.
- ?We measured four roof triangles in Build Lab and tore corners to show 180°.
Measure one angle in each pair with a protractor and work out the other.
Angles everywhere, and one measurement goes a long way. Tomorrow is Build Day: the roof frame goes on.