Angle Chase
Hunt down every missing angle — on lines, in triangles and quadrilaterals, and across parallel lines and polygons — and learn to name the reason for each step, the way examiners want it.
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Angle Chase 🧭
Missing-angle questions are everywhere in GCSE geometry — and the marks come in **two** parts: the right number **and the reason**. A correct angle with no reason drops marks. So for every step, chase the angle *and* name the rule: "angles on a straight line add to 180°", "alternate angles are equal", and so on.
Lines and points ➖
Three facts to start with: • Angles **on a straight line** add to **180°**. • Angles **around a point** add to **360°**. • When two lines cross, **vertically opposite** angles are **equal**. These alone unlock a huge number of diagrams — often as the first step of a longer chase.
Angles on a line
An interactive activity.
Find the vertically opposite angle
An interactive activity.
Name the reason
When two straight lines cross, what is true of vertically opposite angles?
- They are equal
- They add up to 180°
- They add up to 90°
- They add up to 360°
Triangles and quadrilaterals 🔺
Two more essential sums: • The angles in a **triangle** add to **180°**. • The angles in a **quadrilateral** add to **360°**. Watch for **isosceles** triangles (two equal angles) — but only use that if the diagram or question actually tells you it is isosceles. Never assume it from how it looks.
Missing triangle angle
An interactive activity.
Missing quadrilateral angle
A quadrilateral has angles 90°, 90°, 120° and one unknown. What is the missing angle?
- 60°
- 90°
- 120°
- 80°
Across parallel lines 🚊
When a straight line crosses a pair of **parallel** lines, three special pairs appear: • **Corresponding** angles are **equal** — they make an **F** shape. • **Alternate** angles are **equal** — they make a **Z** shape. • **Co-interior** angles **add to 180°** — they make a **C** shape. Spot the F, Z or C and you know the rule — and the reason to write down.
Match the angle rule to its property
- Corresponding angles
- Alternate angles
- Co-interior angles
- Angles around a point
- Equal — form an F shape
- Equal — form a Z shape
- Add to 180° — form a C shape
- Add to 360°
Alternate angles
An interactive activity.
Co-interior angles
A line crosses two parallel lines. One co-interior angle (C shape) is 70°. What is the other co-interior angle?
- 110°
- 70°
- 20°
- 290°
Polygon angles 🔷
For any polygon, the **exterior** angles always add to **360°**. That gives a quick route for a **regular** polygon (all angles equal): • Each **exterior** angle = 360 ÷ n (n = number of sides). • Each **interior** angle = 180 − exterior (they sit on a straight line). For a regular pentagon: exterior = 360 ÷ 5 = 72°, so interior = 180 − 72 = 108°.
Regular hexagon exterior angle
An interactive activity.
Order the method
An interactive activity.
Quote the reasons
Angles around a point add to _____ degrees. The angles in a triangle add to _____ degrees. When a line crosses parallel lines, _____ angles (in a Z shape) are equal.