31. In the given figure o is the center of circle. A,the points on the

1.	31. In the given figure o is the center of circle. A,the points on the circle. AOC-110, FindC and22m and32 The me
Answer» Angle subtended by an arc is twice the angle subtended by it on the circumference in the alternate segment. Here arc ABC makes ∠ AOC = 110° at the center of the circle and ∠ ADC on the circumference of the circle. ∴ ∠ AOC = 2∠ ACD ⇒ ∠ ACD = ½ (∠AOC) ⇒ = ½ × 110° [∠ AOC = 110°] ⇒ ∠ ACD = 55° The opposite angles of a cyclic quadrilateral are supplementary. ABCD is a cyclic quadrilateral and thus, ∠ ACD + ∠ ABC = 180° = 180° – 55° [∵ ∠ ADC = 55°] = 125° ∴ ∠ ABC = 125° ∴ ∠ ACD = 55° and ∠ ABC = 125°

31. In the given figure o is the center of circle. A,the points on the circle. AOC-110, FindC and22m and32 The me

Answer»

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

Here arc ABC makes ∠ AOC = 110° at the center of the circle and ∠ ADC on the circumference of the circle.

∴ ∠ AOC = 2∠ ACD

⇒ ∠ ACD = ½ (∠AOC)

⇒ = ½ × 110° [∠ AOC = 110°]

⇒ ∠ ACD = 55°

The opposite angles of a cyclic quadrilateral are supplementary.

ABCD is a cyclic quadrilateral and thus,

∠ ACD + ∠ ABC = 180°

= 180° – 55° [∵ ∠ ADC = 55°]

= 125°

∴ ∠ ABC = 125°

∴ ∠ ACD = 55° and ∠ ABC = 125°