Question

O is the centre of circle in the picture beside, if angleAPB=80°, Let us find the sum of the measures of angleAOB and angleCOD and answer with reason.​

Answer 1

Answer:

In ΔAPB, sum of all angle is equal to 180°

⇒ ∠PAB + ∠ABP = 180 - ∠APB

⇒ ∠PAB + ∠ABP = 180 – 80 = 100 --------- (1)

Also by the theorem:-

The angle formed at the centre of a circle by an arc, is double of the angle formed by the same arc at any point on circle.

and

Substituting above values in eq. (1)

⇒ ∠AOD + ∠BOC = 200

Also, as the sum of angles around the point is equal to 360°

⇒ ∠AOD + ∠BOC + ∠AOB + ∠COD = 360

⇒ ∠AOB + ∠COD = 360 – 200 = 160°

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