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Year 7 Maths · KS3 notes

Angles, area and perimeter

Clear notes with worked examples, then 4 practice questions with answers. Written by Beyond Tutors tutors for the KS3 National Curriculum.

Angle facts

  • Angles on a straight line add up to 180°
  • Angles around a point add up to 360°
  • Angles in a triangle add up to 180°
  • Vertically opposite angles are equal

Example: a triangle has angles 48° and 75°. Third angle = 180−48−75=57180 - 48 - 75 = 57°

Types of angle

acute: less than 90° right: 90° obtuse: between 90° and 180° reflex: more than 180°

Perimeter

The distance all the way around. Add every side.

Area

  • Rectangle: length × width
  • Triangle: 12×\dfrac{1}{2} \times base × perpendicular height
  • Parallelogram: base × perpendicular height

Example: triangle, base 10 cm, height 6 cm → 12×10×6=30\dfrac{1}{2} \times 10 \times 6 = 30 cm²

Units

Perimeter is in cm; area is in cm² (squared units).

Practice questions

Try each one, then tap to see the answer and why.

  1. Question 1 · Angle facts

    An isosceles triangle has one angle of 40° between its two equal sides. What is each of the other two angles?

    • A40°
    • B100°
    • C70°
    • D140°
    Show the answer

    C: 70°

    180−40=140180 - 40 = 140, shared equally: 70° each.

  2. Question 2 · Angle facts

    Two straight lines cross. One of the angles is 58°. What is the angle vertically opposite it?

    • A32°
    • B122°
    • C58°
    • D302°
    Show the answer

    C: 58°

    Vertically opposite angles are equal: 58°.

  3. Question 3 · Angle facts

    Angles around a point are 95°, 120° and xx. Find xx.

    • A65°
    • B215°
    • C155°
    • D145°
    Show the answer

    D: 145°

    Angles around a point add to 360°: 360−95−120=145360 - 95 - 120 = 145°.

  4. Question 4 · Types of angle

    Which of these is a reflex angle?

    • A89°
    • B200°
    • C179°
    • D90°
    Show the answer

    B: 200°

    Reflex angles are between 180° and 360°.

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