Question

O is the centre of the circle and the measure of arc ABC is 100. Determine angle ADC and angle ABC

Answer 1

Angle subtended by an arc is twice the angle subtended by it on the circumference in the alternate segment.

Here arc ABC makes ∠ AOC = 100° at the center of the circle and ∠ ADC on the circumference of the circle.

∴ ∠ AOC = 2∠ ACD

⇒ ∠ ACD = ½ (∠AOC)

⇒ = ½ × 100° [∠ AOC = 100°]

⇒ ∠ ACD = 50°



The opposite angles of a cyclic quadrilateral are supplementary.

ABCD is a cyclic quadrilateral and thus,

∠ ACD + ∠ ABC = 180°

= 180° – 50° [∵ ∠ ADC = 50°]

= 130°

∴ ∠ ABC = 130°

∴ ∠ ACD = 50° and ∠ ABC = 130°

Answer 2

Answer:

ADC = 50°

ABC=130°

Step-by-step explanation:

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