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Academy11+

11+ Maths · Topic explained

Angles

What do a slice of pizza and the hands of a clock have in common?

The big idea

An angle measures a turn, in degrees. A full turn is 360°.

Picture it

Cut a pizza into 4 equal slices: each corner is a right angle, 90°.

Key words

acute
Less than 90°.
right angle
Exactly 90°, a quarter turn.
obtuse
Between 90° and 180°.
reflex
More than 180°.

Worked examples

  1. 1Warm-up

    Angles on a straight line: 130° and x. Find x.

    • Angles on a straight line add up to 180°
    • x = 180 − 130 = 50°
  2. 211+ standard

    Two angles of a triangle are 65° and 72°. Find the third angle y.

    • Angles in a triangle add up to 180°
    • 65 + 72 = 137
    • y = 180 − 137 = 43°
  3. 311+ standard

    Angles round a point: 100°, 120°, 85° and a. Find a.

    • Angles round a point add up to 360°
    • 100 + 120 + 85 = 305
    • a = 360 − 305 = 55°
  4. 411+ standard

    An isosceles triangle has a top angle of 40°. Find each of the two equal angles.

    • 180 − 40 = 140
    • The two equal angles share it: 140 ÷ 2 = 70° each

The common mistake

The mistake

The angle with the longer lines is the bigger angle.

Instead

An angle's size is the amount of turn between the lines, not how long they are.

Why: Draw a 30° angle with long arms and a 60° angle with short arms: the 60° one is still bigger.

Where it comes up in the 11+

Missing angles: straight line 180°, round a point 360°, triangle 180°, quadrilateral 360°.

The video

Video coming soon

We're making a short video that explains angles step by step. Until then, everything it covers is on this page.

Free printable

Angles worksheet

Practice questions on this topic to print and try on paper, at home or on the way to school.

Download the worksheet (PDF)

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Quick quiz

Have a go first, then tap to see the answer.

  1. 1. What type of angle is 135°?

    • Acute
    • Right
    • Obtuse
    • Reflex
    Show the answer

    Obtuse

    135° is between 90° and 180°.

  2. 2. Two angles in a triangle are 90° and 35°. What is the third?

    • 55°
    • 65°
    • 45°
    • 235°
    Show the answer

    55°

    180 − 90 − 35 = 55.

  3. 3. Three angles of a quadrilateral are 90°, 80° and 100°. What is the fourth?

    • 90°
    • 80°
    • 110°
    • 270°
    Show the answer

    90°

    Angles in a quadrilateral add up to 360°: 360 − 270 = 90.