In the given figure, O is the centre of the given circle and measure of arc ABC is $100^{\circ} .$ Determine $∠ A D C a n d ∠ A B C$

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Solution

ANSWER:We know that the angle subtended by an arc is twice the angle subtended by it on the circumference in the
alternate segment.
Thus, ∠ AOC = 2 ∠ ADC
⇒ 100 ° = 2 ∠ ADC
∴ ∠ ADC = 50 °
The opposite angles of a cyclic quadrilateral are supplementary and ABCD is a cyclic quadrilateral.
Thus, ∠ ADC + ∠ ABC = 180 °
⇒ 50 ° + ∠ ABC = 180 °
⇒ ∠ ABC = (180 ° – 50 ° ) = 130 °
∴ ∠ ADC = 50 ° and ∠ ABC = 130 °

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In the figure, O is the centre of the circle and the measure of arc ABC is 100^o. The measure of angle ABC will be

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