Question

In the joining figure shown XAY is a tangent. If ∠ BDA = 44°, ∠ BXA = 36°.
Calculate: (i) ∠ BAX, (ii) ∠ DAY, (iii) ∠ DAB, (iv) ∠ BCD.

Answer 1

(i) ∠ BAX = ∠ BDA = 44°        ...(Angles in the alternate segment)

(ii) ∠ ABD = ∠ BXA + ∠ BAX
∠ ABD = 36° + 44° = 80°         ....(Ext. angle of a triangle = sum of internal opposite angles)
∴ ∠ DAY = ∠ ABD = 80°           ...(Angles in the alternate segment)

(iii) ∠ DAB = 180° - (∠ BAX + ∠ DAY)
∠ DAB = 180° - (44° + 80°) = 56°

(v) ∠ BCD = 180° - ∠ DAB
∠ BCD = 180° - 56° = 124°         ...(Opposite ∠ s of a cyclic quadrilateral are supplementary)