Question

O is the centre of the circle, work out the value of X.
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Answer 1

69

Explanation:

The central angle is twice the inscribed angle. So the angle that is behind the one equal to 2x is equal to x. We know that the opposite angles in a circle add up to 180. Therefore, we can solve for x:

`x + x + 42 = 180$^(\circ)$\\\\2x = 180$^(\circ)$ - 42$^(\circ)$\\\\2x = 138$^(\circ)$\\\\x = 69$^(\circ)$`