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In the adjacent figure A, B, C are three points on the circle. O is it’s centre. If ∠AOB = 2x° and ∠ACB = 3x – 65°, find the value of x. Give reasons to support your answer.

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From figure ∠ACB = 3x – 65° and- ∠AOB = 2x° 

From theorem, chord \(\overline {AB}\) making angle at centre ∠AOB = 2∠ACB 

∴ 2x = 2(3x – 65°) 

2x = 6x – 130° 

6x – 2x = 130° 

4x = 130°

x = 130°/4 = 32.5°

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