Q) In the given figure, O is the centre of the circle. If Ð AOB = 145°, then find the value of x.

Ans:

Step 1: 

From the given diagram, ∠ AOB = 145⁰

∴ Reflex angle ∠ AOB = 360⁰ – 145⁰ = 215 ⁰

Step 2: By the subtended angle 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.”

Here ADB is the major arc, the angle subtended by the arc at the centre is Reflex angle ∠ AOB, and the angle subtended on the  remaining part of the circle is ∠ ACB.

∴ Reflex angle ∠ AOB = 2 ∠ ACB

∴ ∠ ACB =

By substituting the above value, we get:

∴ X = = 107.5 ⁰

Therefore, the value of ∠ ACB is 107.5 ⁰

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