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Question
If O is the centre of the circle, find the value of x in the following figure
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Solution
We have
∠AOC = 120°
By degree measure theorem
∠AOC = 2∠APC
⇒ 120° = 2∠APC
⇒∠APC= `(120°)/2=60°`
∴∠APC + ∠ABC = 180°
⇒ 60° + ∠ABC = 180°
⇒ -60° +180° = ∠ABC
⇒ ∠ABC = 120°
∴∠ABC + ∠DBC = 180°
⇒120 + x = 180°
⇒ x = 180° -120° = 60°
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