Question

Find the value of x from the given figure, in which O is the centre of the circle.

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Answer 1

Given: $\angle$BAC in a circle with centre 0 is ${40}^{\circ }$.

To find: $\angle$BOC = (say $x^{\circ }$)

Procedure: $\angle$BOC = 2 $\angle$BAC = 2 x ${40}^{\circ }$ = ${80}^{\circ }$

In $△$BOC,
BO = OC (Radii of the same circle)
$\angle$B = $\angle$C = x
x + $\angle$BOC + x = ${180}^{\circ }$ [Sum of angles in a triangle]
2x =${180}^{\circ }$ — $\angle$BOC
2x = ${180}^{\circ }$ — ${80}^{\circ }$
2x = ${100}^{\circ }$
x = ${50}^{\circ }$.