Question

In the given figure ∠BAC = 55°, ∠BCA = 62°, the altitude BE produced meets the circle at D, determine ∠ACD, ∠DAC and ∠ADB

Answer 1

angle ACD = 31 °
as the triangle ADC is half the Triangle BCA

angle DAC is 55°
because the angle BAC is double
so, it become 110°

angle ADB is 145° by adding 90° and 55°
we got this

Answer 2

By Angle Sum Property of a Triangle,

In triangle BAE,

Angle ABE = 180°- 90°- 55°

= 35°

⇒Angle ACD = 35° [ Angles in the same segment are equal ]

Similarly, In triangle BCE,

Angle CBE = 180° - 90°- 62°

= 28°

⇒Angle DAC = 28° [ Angles in the same segment are equal ]

HOPE IT HELPS :-D