Question

In the given figure, $2b-a={65}^o$ and $\angle BOC={90}^o$, find the measure of $\angle AOB,\angle AOD$ and $\angle COD$.

• A. $\angle AOB={35}^o$
• B. $\angle AOD={100}^o$
• C. $\angle COD={135}^o$
• D. All of the above

Answer 1

The correct option is D All of the above

Given,
$\angle BOC={90}^{o}and2b-a={65}^o$
From the figure,
$\angle AOB+\angle AOD+\angle BOC+\angle COD={360}^o$
$=>a+2b+{90}^o+(2a+b+15)={360}^o$
$=>a+b={85}^o$
Add the given equation with this equation, we get
$2b-a+a+b={65}^o+{85}^o$
$b={50}^o$
then, $a={85}^o-b={85}^o-{50}^o={35}^o$
$\angle AOB=a^o={35}^o,\angle AOD=2b^o=2\times {50}^o={100}^o$
$\angle COD=(2a+b+15)=2\times {35}^o+{50}^o+15={135}^o$