Angles

What Your Child Is Learning

Angles measure the amount of turn between two lines that meet at a point. They're measured in degrees, written with a small circle symbol: °.

There are a few landmark numbers worth knowing, because your child will use them constantly:

• Right angle = 90° — the corner of a book, a door frame, or a square. Your child already knows this one instinctively.
• Straight line = 180° — a completely flat line. If two angles sit on a straight line, they must add up to 180°.
• Full turn = 360° — a complete rotation, like spinning all the way round on the spot. All the angles around a single point must add up to 360°.

At KS3, your child moves beyond just measuring angles with a protractor. They start using angle facts — logical rules — to calculate missing angles without measuring anything. This is where angles become more about reasoning and less about equipment.

How Schools Teach It Now

Schools build up angle facts in layers. Each rule is simple on its own; the skill is recognising which rule to use in a given diagram.

Rule 1: Angles on a Straight Line Add to 180°

If two or more angles sit along a straight line, they must add up to 180°. This is probably the most-used angle fact in KS3.

Rule 2: Angles Around a Point Add to 360°

If several angles meet at a single point (like slices of a pie), they must add up to 360°.

Rule 3: Vertically Opposite Angles Are Equal

When two straight lines cross, they create two pairs of equal angles. The angles that are opposite each other (across the point where the lines cross) are always equal. Schools call these "vertically opposite angles" — the word "vertical" here means they share the same vertex (the point where lines meet), not that they're up-and-down.

Rule 4: Angles in a Triangle Add to 180°

The three interior angles of any triangle always sum to 180°. This is true for every triangle, no matter how squashed or stretched.

Your child will often need to combine more than one rule in a single question. For example, they might use "angles on a straight line" to find one angle, then use "angles in a triangle" to find another.

Common Mistakes to Watch For

• Confusing 180° and 360°. "Is it the straight line one or the full turn one?" If in doubt, ask your child to picture it: a straight line is half a turn (180°), a full rotation is a whole turn (360°). Once they can visualise the difference, it sticks.
• Not spotting vertically opposite angles. In a diagram with crossing lines, students sometimes try to calculate angles that are actually just equal to an angle they already know. If two lines cross, the opposite angles are equal — no calculation needed.
• Measuring from the wrong baseline on a protractor. Protractors have two scales (one going each way). Students often read the wrong scale and get an answer that's wildly off. A good check: if the angle is clearly less than 90°, the answer should be less than 90. If it's obviously obtuse, it should be more than 90.
• Forgetting to give reasons. At KS3 and especially at GCSE, students often lose marks for writing just the number. Schools expect a reason: "angles on a straight line add to 180°" or "vertically opposite angles are equal." Encourage your child to always write the rule they used.

Try It Together

Once your child is comfortable with these, try combining rules: "A triangle has a 40° angle and a 60° angle. One side of the triangle continues as a straight line. What's the angle between the straight line and the triangle's third side?" (Answer: the third angle in the triangle is 80°, and the exterior angle on the straight line is \(180° - 80° = 100°\).)

Let Them Practise

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