Question

In the given figure O is the centre of the circle and $\angle OAC={60}^{\circ }$ and $\angle OBC={70}^{\circ }$ Find $\angle AOB$

• A. ${130}^{\circ }$
• B. ${80}^{\circ }$
• C. ${65}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

Answer: (D)

${100}^{\circ }$

$OA=OB=OC=radius$

In $△OAC$

Since $OA=OC$

$\angle OAC=\angle OCA=60$

$⟹\angle ADC=180–60-60=60$

In $△OBC$

Since $OB=OC$

$\angle OCB=\angle OBC=70$

$⟹\angle COB=180–70-70=40$

$\angle AOB=\angle AOC+\angle COB=60+40={100}^{\circ }$