Question

The angle A, B, C and D of a quadrilateral are in the ratio 1 : 2 : 4 : 5. If bisectors of ∠C and ∠D meet of O, the ∠COD = __________.

Answer 1

Let the angle A, B, C and D of a quadrilateral be x, 2x, 4x and 5x, respectively.

We have,
Sum of all the angles of a quadrilateral = 360°
⇒ x + 2x + 4x + 5x = 360°
⇒ 12x = 360°
​⇒ x = 30°

Thus, ∠A = 30°
∠B = 60°
∠C = 120°
∠D = 150°

Now, the bisectors of ∠C and ∠D meet of O
Thus, in ∆COD,
$\frac{1}{2}$∠DCO + ∠COD + $\frac{1}{2}$∠ODC = 180°
⇒ $\frac{1}{2}$ × 120° + ∠COD + $\frac{1}{2}$ × 150° = 180°
⇒ 60° + ∠COD + 75° = 180°
⇒ 135° + ∠COD = 180°
⇒ ∠COD = 180° − 135°
⇒ ∠COD = 45°

Hence, ∠COD = 45°.