Question

Find the value of $(a+b)$.

• A. ${40}^{\circ }$
• B. ${80}^{\circ }$
• C. ${120}^{\circ }$
• D. ${160}^{\circ }$

Answer 1

Answer: (C)

${120}^{\circ }$

Here, $\angle DCF=\angle BCE={30}^{\circ }$ ...(vertically opposite angles)
Now, $\angle ADC=\angle DFC+\angle DCF$ ...(Exterior angle property)
$⟹$ $\angle ADC={30}^o+b$.
Also, $\angle ABC=\angle BCE+\angle BEC$ ...(Exterior angle property)
$⟹$ $\angle ABC={30}^o+a$.
Now, $\angle ADC+\angle ABC={180}^o$ (Opposite angles of cyclic quadrilateral)
$⟹$ ${30}^o+a+{30}^o+b={180}^o$
$⟹$ $a+b={120}^{\circ }$.

Hence, option $C$ is correct.