Angles in the same segment - Higher
Discover updated revision resources for GCSE Maths: Angles in the same segment, with step-by-step slideshows, quizzes, practice exam questions, and more!
The angles at the Circumference is the name of the perimeter of a complete circle, that is, the distance all around it.An angle created by an object at a given point. by the same The curve between two points on the circumference of a circle. are equal.
More simply, angles in the same segment are equal.
Angles \(a = a\)
Example
Calculate the angles \(p\) and \(q\).
Angles in the same segment are equal.
\(p = 52^\circ\)
\(q = 40^\circ\)
Proof
Let the obtuse angle MOQ = \(2x\).
Using the circle theorem, the angle at the centre is twice the angle at the circumference.
Angle MNQ = \(x\) and angle MPQ = \(x\).
Therefore angle MNQ = angle MPQ.
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