Question

In the figure, O is the centre of the circle, ∠D=32°, ∠BXC= 85°. Find:-
a)∠C
b) ∠A
c) ∠DOC

Answer 1

Answer:

In triangle AXD,

Angle D+ Angle DXA+ Angle A= 32°+85°+Angle A=180° [Sum of angle of triangle is 180°]

=> Angle A=180°-117°=63°

Hence, Angle A =63°.

Angle A = Angle B [ Angle in same arc, so they are equal]

So, here, Angle C+ Angle BXC+ Angle B= Angle C+ 85°+63°=180°

=> Angle C= 180°-(85°+63°)=> Angle C=32°.

Hence, Angle C=32°.

Angle BXC+Angle CXD=180°. [ Straight line, therefore sum of angle is 180°]

Angle 85°+Angle DOC= 180°

=> Angle DOC= 180°-85°=95°.

Hence, Angle DOC=95°.

Therefore, a) Angle C=32°

b) Angle A=63°

c) Angle DOC= 95°.

I hope you got your answer.

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