Geometry & measures · Angles & polygons
Chapter 1 · 4
The idea
Angle rules & giving reasons
Why angles at a point make 360°, angles on a straight line make 180°, and vertically opposite angles are equal; the triangle and quadrilateral angle sums; isosceles triangles; and how to write the reasons examiners insist on.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Geometry & measures · Angles & polygons
Angle rules & giving reasons
Why angles at a point make 360°, angles on a straight line make 180°, and vertically opposite angles are equal; the triangle and quadrilateral angle sums; isosceles triangles; and how to write the reasons examiners insist on.
Why it works
An angle measures turn
An angle measures turn. A full turn is , so angles meeting at a point share out the full turn: angles at a point add up to 360°. A straight line is exactly half a turn, so angles on a straight line add up to 180°.Vertically opposite — and why
When two straight lines cross they make four angles. Call two neighbouring ones and : they sit on a straight line, so . But and the angle opposite also sit on a straight line, so that opposite angle is . The two angles facing each other across the crossing are forced to be equal.Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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