Chain several angle facts together, with a reason for each step, including algebra, ratios and polygons.
What you will learn
- Combine angle facts in several steps
- Give a reason for each step
- Solve angle problems with algebra and ratio
One fact at a time
Three letters name an angle: angle ABC is the angle at B, the middle letter, between the lines BA and BC.
So in triangle ABC, angle BAC is the angle at A.
Mark each angle you find on the diagram, and write its reason. Typical chain: alternate angles give one angle, the isosceles triangle gives a second, angles in a triangle give the third.
- AB is parallel to CD; triangle PQR has PQ = PR; the angle between AB and PQ at P is 50°, alternate with angle PQR
- angle PQR = 50° (alternate angles are equal)
- angle PRQ = 50° (base angles of an isosceles triangle are equal)
- angle QPR = 180 − 50 − 50 = 80° (angles in a triangle add up to 180°)
Not drawn accurately
If side BC of triangle ABC is extended beyond C to D, angle ACD is on a straight line with angle ACB, so ACD = 180 − ACB. It also equals A + B, the exterior angle fact.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- One fact at a time
- Inside polygons and zigzags (Higher)
- Ratios and algebra
7 practice questions, marked as you go; about 25 minutes in all.
Key terms
Angle ABC
In this unit: Angles, polygons and parallel lines
Angle facts on lines, at points and in triangles, angles with parallel lines, quadrilaterals, interior and exterior angles of polygons, and chains of reasoning.