Question

In the diagram, the points $A,B$ and $C$ lie on a circle with centre $O$. $\angle BOC={120}^o$ and $\angle ACO={42}^o$. The magnitude of $\angle ABO$ is

• A. ${18}^o$
• B. ${20}^o$
• C. ${22}^o$
• D. ${24}^o$
• E. ${48}^o$

Answer 1

The correct option is A ${18}^o$

Given angle $BOC={120}^0$ and angle $AC={42}^0$

The angle subtended by chord $BC$ at $A$ is $\frac{120}{2}={60}^0$

Angle $OBC=$ angle $OCB={30}^0$

In triangle $ABC$ , angle $ABO=180-42-30-30-60=180-162=18$

Therefore correct option is $A$