Question

The figure given below, shows a circle with centre O. Given : ∠AOC = a and ∠ABC = b. 

1. Find the relationship between a and b.

2. Find the measure of angle OAB, if OABC is a parallelogram.

Answer 1

i. ∠ABC = `1/2` Reflex (∠COA)

(Angle at the centre is double the angle at the circumference subtended by the same chord)

`=> b = 1/2 (360 - a)` 

`=>` a + 2b = 360°

ii. Since OABC is a parallelogram, so opposite angles are equal.

2b + b = 360° 

3b = 360°

b = 120°

∴ 120° + 120° + x + x = 360°

2x = 360° – 240°

2x = 120°

`x = (120^circ)/2`

x = 60°

`=>` ∠OAB = 60°