Question

In the figure, if $\angle BOC=7x+{20}^o$ and $\angle COA=3x$, then the value of $x$ for which $AOB$ becomes a straight line is:

• A. ${16}^o$
• B. ${14}^o$
• C. ${20}^o$
• D. ${21}^o$

Answer 1

The correct option is A ${16}^o$

$\angle AOB=\angle BOC+\angle COA$
$=7x+{20}^o+3x=10x+{20}^o$
$AOB$ becomes a straight line if $\angle AOB={180}^o$, i.e.,
$10x+{20}^o={180}^o$ $\Rightarrow$ $10x={160}^o$
$\Rightarrow$ $x={16}^o$.