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Solving Angle Problems with Reasoning
Rung 2 of 4 · The method

Setting It Out with Reasons

A number on its own is worth almost nothing. A number plus the reason is worth full marks. Let's make writing the reason as automatic as the working.


PractiseRead the diagram, type your angle, pick the reason, then check. You need both right.
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Every angle answer you write should look the same shape: angle = number, reason. That's the whole method. The number comes from the maths; the reason comes from naming the fact you used.

The Three Moves

One — read the diagram, not the picture. Look at the marks: arrows mean parallel, ticks mean equal, the little square means 90°. The angle facts you're allowed to use depend entirely on what's marked.

Two — do the calculation. Spot which fact connects your known angle to the unknown, and run it. Sometimes that's a subtraction (180 − 70), sometimes it's just "they're equal".

Three — write the reason beside it. Not in your head — on the page. "Co-interior angles, parallel lines." "Vertically opposite angles are equal." The reason is a mark.

A Worked One, Set Out Properly

Two parallel lines, a transversal, one angle marked 110° on the inside. Find x on the inside below it:

x = 180° − 110° = 70°  (co-interior angles, parallel lines)

That single line earns both marks: the right value and the named reason. Leave the reason off and you've thrown half the marks away even with the right number.

Say it plainly: never write a lonely number. The format is always x = … , because …. The "because" is not optional — it's where the marks are.

Learn the Reasons Word-for-word

Examiners want the proper phrase, not a vague gesture. "Co-interior angles, parallel lines." "Corresponding angles, parallel lines." "Alternate angles, parallel lines." "Angles on a straight line." "Vertically opposite angles." Drill them in the toy — it checks the number and the reason separately, so you'll feel straight away when one's missing.

Us, Thinking Out Loud

Can you say all five reason-phrases without peeking?

Why does a right answer with no reason only get half the marks?