Question

abcd is a cyclic quadrilateral angle CBQ =51and y =2x .find the value of and y

Answer 1

abcd is a cyclic quadrilateral angle CBQ =51and y =2x. The value of and y is 78°

Given,

ABCD is a cyclic quadrilateral

∠ CBQ = 51°

y = 2x

In  Δ APB,

∠ A = 90°  (AD ⊥ AQ)

∠ B = 51°  (vertically opposite angles are same)

as we know that, the interior angles of a triangle equals 180°, we have,

∠ A + ∠ B + ∠ P = 180°

90° + 51° + x = 180°

141° + x = 180°

x = 180° - 141°

∴ x = 39°

y = 2x  (given)

y = 2 × 39°

∴  y = 78°