Question

O is the centre of a circle and AB a diameter. ABCD is a cyclic quadrilateral. AngleABC = 65° AngleDAC= 40°, then the measure of BCD is (a) 75° (b) 105° (c) 115° (d) 80°​

Answer 1

Answer : 115°

Explaination:

Given:

∠ABC=65°

∠DAC=40°

∠BCD= ??

∵ ∠ACB is angle in a semicircle.

∴ ∠ACB = 90°

∵ ∠ABC and ∠ADC are supplementary angles ( as the sum of opposite angles of a cyclic quadrilateral is 180° ).

∴ ∠ABC + ∠ADC = 180°

⇒ 65°+∠ADC = 180°

⇒ ∠ADC = 180°- 65°

⇒ ∠ADC = 115°

In Δ ADC,

∠ADC = 115°, ∠DAC = 40°

∴ ∠DAC = 180°-∠ADC-∠DAC

= 180°- 115°- 40°

= 65°- 40°

= 25°

∴ ∠BCD = ∠ACB+∠DCA

= 90°+25°

= 115°

Answer 2

Step-by-step explanation:

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