Tuesday
Tuesday: Write the Equation
Raven tapes three straws to the beam, fanned out like a hand. "Three angles along the beam. 40, 65 and one more."
"Three angles, still a straight line," Rocket says. "So they still make 180. 40 plus 65 plus the mystery."
"Write it before you solve it," Raven says. "What do you notice when you use a letter?"
Rocket writes 40 + 65 + x = 180. "105 + x = 180. x is 75."
"Now this one." Raven draws a square corner split by one line. "One part is twice the other."
Nova hovers over the drawing, her light resting on the corner. "Call the small one x," she says. "What is the big one?"
"2x. And x + 2x = 90. So 3x = 90, x = 30." Rocket grins. Nova hums. "Write, then solve. Every time."
From a picture to an equation
- Name the pair: straight line (180), square corner (90), full turn (360), or vertical (equal).
- Call the unknown angle x. If another angle is described from x, write it too: 2x, x + 10.
- Write the equation: the angles added equal the whole.
- Solve it one step at a time. Then check: do the angles add back up to the whole?
| Picture | Equation | Solution |
|---|---|---|
| 40° and x along a straight line | x + 40 = 180 | x = 140 |
| 40°, 65° and x along a straight line | x + 40 + 65 = 180 | x = 75 |
| x and 2x fill a square corner | x + 2x = 90 | x = 30 |
| x and x + 30 along a straight line | x + x + 30 = 180 | x = 75 |
| x, 90° and 150° around a point | x + 90 + 150 = 360 | x = 120 |
Check the last row: 120 + 90 + 150 = 360. All the way around a point is a full turn, 360°.
Check the square corner: x = 30, so 2x = 60, and 30 + 60 = 90. The check is part of the method.
- Read the question.
- Tap your answer.
- Read the question.
- Tap your answer.
The two angles are supplementary. One is 125°. What is the other, in degrees?
The two angles are complementary. One is 62°. What is the other, in degrees?
The two angles are adjacent and make 120° together. One is 48°. What is the other, in degrees?
The two angles are vertical. One is 37°. What is the other, in degrees?- Read the question.
- Tap your answer.
| Statement | True or false? |
|---|---|
| 40 + 65 + 75 = 180 | ? |
| 30 + 60 = 90 | ? |
| Angles all the way around a point add to 180°. | ? |
| If one angle is 2x and the other is x, the bigger one is twice the smaller. | ? |
Write the equation for the third angle and solve it. Then measure to check.
Masking tape goes on paper or the table top, never across the floor.
Write, then solve. Tomorrow is Build Lab: the protractor meets the roof triangles.