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Maths: Shapes and Angles

▶  Watch: how to answer a shapes and angles question6 min

Four steps in about six minutes — one real question, worked step by step, then the traps to watch out for.

In these questions, you're given a shape, or some angles. For a shape, you're asked which name or fact fits it. For angles, you're asked how big one is.

Often, the question asks which one does NOT fit. There are five answers to choose from.

In GL's papers, a shape question comes down to testing each option against a fact. The video above and the worked example below work through the same question, with the options in the same order. The angle question after it is the video's second question.

The method

Four steps: spot what's asked, name the facts, test every option, trust the marks.

  1. Step 1 of 4

    Spot what's asked

    Is it about a shape or an angle? Which one? And does it say NOT?
  2. Step 2 of 4

    Name the facts

    Think about each shape: which sides are parallel, which are equal, and which corners are right angles? For angles, a straight line makes 180°.
  3. Step 3 of 4

    Test every option

    Check each one against the facts. For an angle, do one sum.
  4. Step 4 of 4

    Trust the marks

    There's no measuring in the test, so go by the marks and the numbers, never by how a shape looks.

Worked example

Dylan writes five facts about shapes, but one of them is wrong. Which statement is NOT true?

A. A pentagon has 5 sides. B. Every square is a regular polygon. C. Every parallelogram has 4 right angles. D. A rhombus has 4 equal sides. E. An octagon has 8 sides.

  1. Spot what's asked. These are facts about shapes, and the question says NOT. So four of the facts are true, and one is not. We want the one that's not true, so we cross off the four that are.
  2. Name the facts. A square has four equal sides and four right angles. A rhombus has four equal sides as well. A parallelogram has two pairs of parallel sides. And a pentagon has five sides, an octagon eight.
  3. Test every option. Check each statement against the facts. A pentagon has five sides. That's true, so cross off A. Every square is a regular polygon: regular means all its sides are equal and all its angles are equal, and a square's are. True, so B is out. A rhombus has four equal sides. True, so D is out. An octagon has eight sides. True again, so E is out. That leaves C: every parallelogram has four right angles. Picture a parallelogram drawn upright, and it looks as if it does.
  4. Trust the marks. A parallelogram's arrows only say that its opposite sides are parallel. Nothing marks its corners as right angles. And a parallelogram can lean. Picture it pushed over: its opposite sides stay parallel, but one corner is now 120°. So not every parallelogram has four right angles, and C is not true. So the answer is C.

Answer: C — Every parallelogram has 4 right angles. (not every parallelogram has 4 right angles)

A second worked example: angles

The diagram shows three angles on a straight line. How many degrees is angle x?

A straight line, with two lines going up from one point on it. They make three angles side by side: 50° on the left, x in the middle and 35° on the right.

A. 145° B. 95° C. 275° D. 85° E. 35°

  1. Spot what's asked. The angle x, on a straight line with 50° and 35°.
  2. Name the facts. A straight line makes 180°.
  3. Test every option. With one sum. Add the angles you know: 50 + 35 = 85. Take that away from 180, and you get 95. D is 85°, but that's only the two angles added, so D is out. A is 145°, which is 180 − 35, with the 50 left out. So A is out. C is 275°, which takes 85 from 360. That's a whole turn, not a straight line, so C is out. And E is 35°, an angle you were given, so E is out too.
  4. Trust the marks. Check the numbers: 50 + 95 + 35 = 180. So the answer is B.

Answer: B — 95° (180 − (50 + 35) = 95)

Things to watch out for

  1. Parallel or perpendicular? Parallel lines go the same way, and never meet. Perpendicular lines meet at a square corner. One question asks which line is perpendicular to line P. Line R would meet it at a square corner. Line Q is parallel to P. That's the other word, and it's one of the answers too.
  2. Know the size bands. Less than a right angle is acute. Between a right angle and a straight line is obtuse. More than a straight line is reflex. One question asks which of 76°, 90°, 95°, 180° and 198° is obtuse, so it's 95°. Next door, 90° is a right angle, and 180° is a straight line: neither is obtuse.
  3. Don't assume a right angle. Only a square mark means 90°. In the second question, x looks close to a right angle. But there's no square mark, and the numbers make it 95°. Only a square in the corner means 90°.
  4. A turned shape keeps its name. Its marks name it, whichever way up it is. One question asks for the name of a quadrilateral that is drawn turned, so it doesn't sit the way you might expect. But its arrows mark one pair of parallel sides, and only one pair, so it can't be a parallelogram. Picture it turned until those sides are level. It's a trapezium, whichever way up it is.

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