The exterior angle of a triangle
Change two angles of a triangle and watch the third. Carry one side on past a corner, and find that the angle outside it equals the two opposite angles inside put together.
Core concept
The three angles of a triangle add up to 180°, and an exterior angle equals the sum of the two interior angles opposite it
Topic: Triangles
The three angle: The amount of turn between two lines that meet, measured in degrees (°). All key words inside any triangle add up to 180°, so if you know two, you can find the third: C = 180° − A − B. Now carry the side BC on past C to a point D. The angle ACD, outside the triangle, is an exterior angle. It makes a straight line with C, so ACD = 180° − C. But 180° − C is just A + B. So an exterior angle equals the two interior angles opposite it put together. This is the exterior angle property, and it gives a quick way to find angles in roofs, ladders and bridges.
What you will learn
- Use the angle sum of a triangle to find a missing angle.
- Explain why an exterior angle equals the sum of the two opposite interior angles.
- Use the exterior angle property to find unknown angles.
Before you start
- Know that the angles on a straight line add up to 180°.
Materials
- Paper, scissors, a ruler and a protractor
Equipment
- None
Procedure
- Record a triangle with A = 60° and B = 50°.
- Make C a right angle and record.
- Make C an obtuse angle and record.
- Record a triangle with A = B = 60°.
How this simulation is simplified
- The triangle is flat and its sides are straight.