Circle theorems: angle at the centre

The Maths Habit

Which angle is bigger, the one at O or the one at C? By how much?

OABC O is twice C

The angle at the centre is twice the angle at the circumference

Find x.

O35°x
centre = 2 × circumference
70angle at centre= 2 ×35angle at circumference
x =70°

Find x.

Ox110°
110angle at centre= 2 ×55angle at circumference
x =55°

Find x.

O35°x
centre = 2 × circumference
70angle at centre= 2 ×35angle at circumference
x =70°

Find x.

O48°x
96angle at centre= 2 ×48angle at circumference
x =96°

Circle theorems: angle at the centre worksheet, page 1

Answer sheet

  1. The angle at the centre is 4x. The angle at the circumference is x + 20. Find x.

    20

  2. The angle at the centre is 180°. What is the angle at the circumference?

    90°

  1. O is the centre. Find angle x.

    x = 104°
    ABCO52°x

  2. O is the centre. Find angle y.

    y = 62°
    ABCOy124°

  3. Angle at the centre 64°. Jo says the angle at the circumference is 128°. Correct Jo.

    Doubled, not halved: 32°
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