Question

In a cyclic quadrilateral ABCD, if m ∠A =3(m∠C). Find m∠A.

Answer 1

In a cyclic quadrilateral ABCD, if m ∠A =3(m∠C). Find m∠A.

Given,

ABCD is a cyclic quadrilateral.

So we have, the sum of the opposite angles is 180°

∴ ∠ A + ∠ C = 180°

m ∠A = 3 (m ∠C)   (given)

Now, we have,

∠ A + ∠ C = 180°

3x + x = 180°

4x = 180°

x= 45°

m∠ C = 45°

∴ ∠ A = 3x = 3 × 45°

∴ m∠ A = 135°