Question

In the given figure, $\angle AOC$ and $\angle BOC$ form a linear pair. If $a-2b={30}^{\circ }$, find a.

• A. ${115}^{\circ }$
• B. ${150}^{\circ }$
• C. ${130}^{\circ }$
• D. ${140}^{\circ }$

Answer 1

The correct option is C ${130}^{\circ }$


Given: $a-2b={30}^{\circ }$
Since $\angle AOC$ and $\angle BOC$ form a linear pair of angles,
$a+b={180}^{\circ }$

So we have these two equations
$a-2b={30}^{\circ }$ (i)
$a+b={180}^{\circ }$ (ii)

On subtracting (ii) from (i) we get
$-3b=-{150}^{\circ }$
$\Rightarrow b=\frac{{150}^{\circ }}{3}$
$\Rightarrow b={50}^{\circ }$

On substituting value of b in (ii) we get
$a+{50}^{\circ }={180}^{\circ }$
$\Rightarrow a={180}^{\circ }-{50}^{\circ }={130}^{\circ }$
$\Rightarrow a={130}^{\circ }$