In $ \Delta A B C, A D $ is perpendicular to $ B C $ and $ O $ is circumcentre of $ \Delta A B C \cdot \angle B=55^{\circ}, \angle A=80^{\circ} . $ Find $ \angle D A O $

Question

In $ \Delta A B C, A D $ is perpendicular to $ B C $ and $ O $ is circumcentre of $ \Delta A B C \cdot \angle B=55^{\circ}, \angle A=80^{\circ} . $ Find $ \angle D A O $, $ 5^{\circ} $, $ 10^{\circ} $, $ 15^{\circ} $, $ 20^{\circ} $

MARKS App · Accepted Answer

∠ D A O = ∠ D A C - ∠ O A C = 90 ° - C - 90 ° - B = B - C Now, by angle sum property of a triangle A + B + C = 180 ° ⇒ C = 180 ° - 55 ° + 80 ° = 45 ° Therefore, ⇒ B - C = 55 ° - 45 ° = 10 °

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