Circle theorems: angles in the same segment

The Maths Habit

Which angle is biggest: the one at P, at Q or at R?

PQRAB They are all equal

Angles in the same segment are equal

Equal or not?

ABCD Equal

Equal or not?

ABCD Not always

Find x and y.

40°xCDAB25°y
x =40°same segment as angle C
y =25°same segment as angle A

Find x and y.

x58°CDABy35°
x =58°same segment as angle D
y =35°same segment as angle B

Find x and y.

40°xCDAB25°y
x =40°same segment as angle C
y =25°same segment as angle A

Find x and y.

2x70°CDAB48°y
2x =70°same segment as angle D
x =35°
y =48°same segment as angle A

Circle theorems: angles in the same segment worksheet, page 1

Answer sheet

  1. Angles in the same segment are x + 30 and 3x. Find the size of each angle.

    45°

  2. The angle at the centre on a chord is 80°. Find the angles at the circumference on the same chord.

    40°

  1. Find angle x.

    x = 47°
    ABCD47°x

  2. Find angle y. Give a reason.

    y = 31°, same segment as BAC
    ABCD31°44°y

  3. Angle ACB is 2x + 25 and angle ADB is 4x − 15. Find the size of angle ACB.

    65°
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