Find angles step by step and give the named angle fact for every step, as questions that say "give reasons" expect.
What you will learn
- Work through a chain of angle facts
- Name the reason for each step in the standard wording
- Spot a wrong reason in someone's working
- Use algebra with angle facts
The reasons, word for word
When two straight lines cross, the angles opposite each other at the crossing are vertically opposite angles.
When a question says "give reasons", each step needs the angle fact written out. Learn these as phrases:
- Angles on a straight line add up to 180°.
- Angles around a point add up to 360°.
- Vertically opposite angles are equal.
- Angles in a triangle add up to 180°. Angles in a quadrilateral add up to 360°.
- Base angles of an isosceles triangle are equal.
- Alternate angles are equal. Corresponding angles are equal. Co-interior angles add up to 180°.
- Exterior angles of a polygon add up to 360°.
"Z angles" or "F angles" do not score: write alternate or corresponding.
In an isosceles triangle, the two base angles share what is left after the top angle: a top angle of 40° gives base angles of (180 − 40) ÷ 2 = 70° each, not 140°.
The rest of this lesson and its 9 practice questions are locked.
In this lesson
- The reasons, word for word
- One step, one reason
- Polygons
- Parallel lines
- Angles with algebra
- Try it: An easy one first
9 practice questions, marked as you go; about 30 minutes in all.
In this unit: Problem solving and proof
Reasoning and problem solving: multi-step money problems, angle chains with reasons, interpreting and justifying with statistics, algebraic proof, and mixed problems across topics.
- Number and money problems
- Angle reasoning with reasons
- Interpret, justify and show that
- Proof and show that
- Mixed exam problems