Question

ABCD is a cyclic quadrilateral find angle BAC angle D=61°​

Answer 1

Given, ABCD is a cyclic quadrilateral in which AD∣∣BC

And, ∠ADC=110∘,∠BAC=50∘

We know that,

∠B+∠D=180∘ [Sum of opposite angles of a quadrilateral]

∠B+110∘=180v

So,∠B=70∘

Now in ΔADC, we have

∠BAC+∠ABC+∠ACB=180∘

50∘+70∘+∠ACB=180∘

∠ACB=180∘−120∘=60∘

And As AD∣∣BC we have

∠DAC=∠ACB=60∘

Now in ΔADC,∠DAC+∠ADC+∠DCA=180∘

60∘+110∘+∠DCA=180∘

Thus,

∠DCA=180∘−170∘=10∘

Explanation:

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