Question

In the given below the figure, AB is parallel to DC, ∠BCD = 80° and ∠BAC = 25°, Find 
(i) ∠CAD, (ii) ∠CBD, (iii) ∠ADC.

Answer 1

(i) ∠CAD = ∠BCE - ∠CAB
∴ ∠CAD = 80° - 25°
∴ ∠CAD = 55°
∵ Ext. of cyclic is equal to opp. int

(ii) ∠CBD = ∠CAD = 55°      ...(Angles in the same segment)

(iii) ∠ ADC = 180° - ∠ DAB
∴ ∠ ADC = 180° - 80°
∴ ∠ ADC = 100°.