Geometry and measuresGCSE Higher

Angles subtended by the same chord, with their vertices in the same segment, are equal

Recognise the theorem, follow two examples, then try five questions.

  • Both vertices must lie on the same side of the chord.

The theorem

Angles subtended by the same chord, with their vertices in the same segment, are equal.

Example 1

With numerical values

, , and lie on the circle. Find the angle .

Angles in the same segment are equal.

Example 2

With algebra

, , and lie on the circle. Find . Each labelled expression is an angle in degrees.

Angles in the same segment are equal.Collect like terms.
Substitute the value of .
Labelled angles

Your turn

Question 1

Find angle .

Check answer
Angles in the same segment are equal.
Question 2

Find the value of .

Check answer
Angles in the same segment are equal.Collect like terms.
Substitute the value of .
Labelled angles
Question 3

Find angle .

Check answer
Angles in the same segment are equal.
Question 4

Find the value of .

Check answer
Angles in the same segment are equal.Collect like terms.
Substitute the value of .
Labelled angles
Question 5

Find angle .

Check answer
Angles in the same segment are equal.
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