Recognise angle measure as additive; find unknown angles by adding or subtracting on a diagram using equations with a symbol for the unknown
You already know that angles on a straight line add up to 180 degrees, and angles all the way around a point add up to 360 degrees. Now you can use those facts to find an angle you don't know yet. Give the missing angle a letter, like x, and write an equation. Then solve it.
Angle measure adds up. When an angle is split into parts, the parts add together to make the whole angle. Turn that around and you get a missing part: whole angle minus the part you know. Watch which total you use. If the whole angle is given to you, that number is the total, not 180 and not 360.
Two angles sit next to each other on a straight line. One angle is 40°, and the other is x°. Since the two angles together make a straight line, write 40 + x = 180. Subtract 40 from both sides: x = 140°.
Three angles meet at a point. Two of them are 130° and 140°, and the third is x°. Angles all the way around a point add to 360, so write 130 + 140 + x = 360. That is 270 + x = 360, so x = 90°.
When an angle is missing, first find the total: 180° for a straight line, 360° for angles around a point. Then subtract the angles you already know. What's left over is your missing angle.
Give the unknown angle a letter, write an equation using the total, and solve for it.
You have found missing angles from the totals they must make: 180 on a straight line, 360 around a point. Now give the missing angle a letter, x, and write an equation. A drawbridge tilts up 65° from the flat road.
The bridge's angle and the angle above it sit on one straight line. Which equation matches?
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24 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.