Question

Find the value of x in the following figure, where O is the centre of the circle:

Answer 1

Step 1: Understand the two given angles

The 100° mark represents the central angle between OB and OA:
∠AOB = 100°.

The 150° mark represents the central angle between OA and OC:
∠AOC = 150°.

Step 2: Find the remaining central angle BOC.

The total angle around point O is 360°.

∠BOC = 360° − 250° = 110°

Step 3: Find angle x = ∠BAC

Angle x at A is an inscribed angle that subtends arc BC.

Inscribed angle = `1/2` × central angle of same arc

Arc BC corresponds to central angle BOC = 110°:

x = `(110°)/2 = 55°`

x = 55°