In the figure, O is centre of the circle. What is the measure of ∠ABC?

The correct answer is Option (2) → 105°

The angle at the centre is twice the angle at the circumference standing on the same arc. ∠ABC stands on the arc AC that does not contain B, the upper arc in the figure.

• The 150° at O opens towards B, so it stands on the lower arc AC.

• The angle at O on the upper arc: \(360^\circ-150^\circ=210^\circ\)

• \(\displaystyle\angle ABC=\frac{210^\circ}{2}=105^\circ\)

Tip: When B lies inside the marked centre angle, ∠ABC is half of the reflex angle and so more than 90°. Half of 150°, that is 75°, is the angle at a point on the other (upper) arc.