Question

In the adjoining figure. A, B, C are three points on a circle O. If $\angle$AOB = 90${}^{\circ }$ and $\angle$BOC = 120${}^{\circ }$, then $\angle$ABC in degree is -

• A. 60
• B. 75
• C. 90
• D. 30

Answer 1

The correct option is B

75

$\angle$AOC = 360${}^{\circ }$ - ($\angle$AOB + $\angle$BOC)

$\angle$AOC = 360${}^{\circ }$ – (90${}^{\circ }$+120${}^{\circ }$) = 150${}^{\circ }$

$\therefore$ $\angle$ABC = $\frac{1}{2}$×$\angle$AOC = 75${}^{\circ }$

[The angle subtended by a chord at the centre of a circle is twice the angle subtended by the same chord at any other point on the remaining part of the circle.]