Answer :

__Theorem:__

__The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.__

(i) In the circle, let us draw a __minor arc__ PR, which subtends an angle ∠ POR = 160° at the centre. Then, from the theorem, the angle at any other part will be

(ii) Here, AB is the major arc. It subtends an ∠ 220° at the centre, then, in its minor segment, the angle at any point will be half of 220°

(iii) __The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.__

From the figure (i), (ii) and (iii), ∠APB = 1/2 ∠AOB

(iv) Draw an angle 144° at the centre. Then, all angles on one part, one and a half times the angles on the other.

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