# Find $x$ of $\angle A O C=70^{\circ}$ and $\angle B A O=50^{\circ}$ where 0 is centre of the circle. (a) $35^{\circ}$ (b) $30^{\circ}$ (c) $25^{\circ}$ (d) $15^{\circ}$

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Find $x$ of $\angle A O C=70^{\circ}$ and $\angle B A O=50^{\circ}$ where 0 is centre of the circle. (a) $35^{\circ}$ (b) $30^{\circ}$ (c) $25^{\circ}$ (d) $15^{\circ}$

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by (40 points)

## Consider △ABO,

AO=BO

⇒∠BAO=∠ABO=300

Consider △CBO,

CO=BO,

⇒∠BCO=∠CBO=400

⇒∠ABC=∠ABO+∠CBO=300+400=700

The angle subtended at the centre is twice the angle subtended anywhere on the arc,

so,

∠AOC=2×∠ABC=140.0

Hope this helps!