Geometry Problem Solving (11+ Style)

G20Geometry Problem Solving

Chain the angle facts, exam style.

Real geometry questions combine two or three facts — solve them one step at a time.

Find angle x: an isosceles triangle sits on a straight line, with 130° outside.

On the line: 180 − 130 = 50° (base angle)

Isosceles: other base angle = 50°

In the triangle: x = 180 − 50 − 50 = 80°

Three facts chained: line 180° → isosceles pair → triangle 180°.

Learn the 4-Step Method

1List your facts.

Line 180° · point 360° · triangle 180° · quadrilateral 360° · vertically opposite equal · isosceles pair equal.

fact list 📋

2Find an angle you CAN get.

Don't stare at x — fill in any angle the facts allow.

start anywhere

3Chain forward.

Each new angle unlocks the next. Write each one on the diagram.

50 → 50 → 80

4Check the totals.

Triangle angles must total 180°; angles on each line 180°.

✓

💡 Key IdeaWrite every angle you find on the diagram — the route to x appears by itself.

Worked Example

Two lines cross. One angle is 40°. A triangle uses the vertically opposite angle and has another angle of 75°. Find its third angle.

Vertically opposite

The triangle’s first angle

40°

→

Triangle total

180 − 40 − 75 = 65

→

✓ Answer

65°

40 + 75 + 65 = 180 ✓

Watch Out! Common Mistakes

Hunting x directly.

Don’t freeze! If x isn’t reachable yet, find ANY other angle first — chains start where the facts work.

Assuming angles look equal.

Never measure by eye! Diagrams are ‘not drawn to scale’. Only use marked values and angle facts.

Skipping the final check.

Ten seconds! Add your triangle’s angles: if they don’t make 180°, a step went wrong — better to know now.

⬇ Cheat Sheet

GEOMETRY PROBLEM SOLVING

List the angle facts before starting.
Fill in ANY findable angle; write it on the diagram.
Chain until x falls out.
Verify totals at the end (180°/360°).

Example: 130° outside → 50° base → isosceles pair → x = 80°.

📄 Free printable: Download the Geometry Problem Solving cheat sheet (PDF) — keep it by your child's desk.

Quick summary

List the angle facts, then find any angle you can — not necessarily x first.
Write each discovered angle on the diagram and chain forward.
Never judge angles by eye; diagrams aren't to scale.
Check totals (180° / 360°) before moving on.

Frequently asked questions

How should children approach multi-step angle problems?

Start by finding any angle the facts allow, write it on the diagram, and chain forward — the path to the target angle reveals itself.

Why can't you trust how the diagram looks?

Exam diagrams are usually not drawn to scale, so an angle that looks like 45° may be anything. Only marked values and angle rules count.

Which facts come up most in 11+ geometry?

Angles on a line (180°), in a triangle (180°), around a point (360°), vertically opposite angles, and the isosceles equal-pair — the exact chain practised in this lesson.

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Geometry Problem Solving