Understanding angles (age 11+)
Apply the properties of angles at a point (360°), on a straight line (180°), and vertically opposite angles to find unknown angles in multi-step problems
What a learner can do afterwards
- Find a missing angle using the fact that angles on a straight line sum to 180°
- Use vertically opposite angles are equal to set up and solve an equation for an unknown
- Combine multiple angle facts in a single diagram to find several missing angles step by step
The lesson
You already know how to measure angles and use angle facts in triangles. Now you will use two more facts to solve trickier problems. Angles on a straight line always add up to 180°. Angles that go all the way around one point always add up to 360°.
When two straight lines cross, they make an X shape with four angles. The two angles that sit directly across from each other, not touching, are called vertically opposite angles. Vertically opposite angles are always equal, no matter how the lines are tilted.
Two lines cross and one angle is 70°. The angle vertically opposite it is also 70°, because vertically opposite angles are equal. The angle right next to the 70° angle sits with it on a straight line, so it must be 180° - 70° = 110°. The fourth angle is vertically opposite that one, so it is 110° too.
In a multi-step problem, find one angle first, then use it to unlock the next one. Look for a straight line, then look for an X shape, and write down each angle as you go.
Angles on a straight line add to 180°, vertically opposite angles are equal, and you can chain these two facts to find every angle in a diagram.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.