Question

In the given figure, if $\angle AOC={110}^o$, then the values of $\angle D$ and $\angle B$, respectively are:

• A. ${55}^o,{125}^o$
• B. ${55}^o,{110}^o$
• C. ${110}^o,{25}^o$
• D. ${125}^o,{55}^o$

Answer 1

Answer: (A)

${55}^o,{125}^o$

Given, $\angle AOC={110}^o$.
By property of circles, we have $\angle AOC=2\angle ADC$
$\Rightarrow \angle ADC={110}^o÷2={55}^o$

$\Rightarrow$ $\angle D={55}^o$.

Also, $\angle B+\angle D={180}^o$ ...[Opposite angles of cyclic quadrilateral are supplementary]
$⟹$ $\angle B={180}^o-\angle D={180}^o-{55}^o={125}^o$.

Hence, option '$A$ is correct.