In the figure given below, if $\angle \mathrm{AOC}$ and $\angle \mathrm{BOC}$ and form a linear pair such that $\left(\mathrm{a}-2\mathrm{b}\right)={30}^{°},$form a linear pair such that then what are the measures of angles $\mathrm{a}$ and $\mathrm{b}$?

 

It is given that $\mathbf{\angle }\mathbf{AOC}$  and $\mathbf{\angle }\mathbf{BOC}$ form a linear pair such that $\left(a-2b\right)\mathbf{=}{\mathbf{30}}^{\mathbf{°}}\mathbf{.}$

Using the linear pair property, we have:

$\angle \mathrm{AOC}+\angle \mathrm{BOC}={180}^{°}$
$\mathrm{a}+\mathrm{b}={180}^{°}\text{ ...}\left(1\right)$
Given, $\left(\mathrm{a}-2\mathrm{b}\right)={30}^{°}....\mathrm{(2)}$

Subtracting the equation (2) from (1), we get:
$\begin{array}{l}3\mathrm{b}={150}^{°}\\ \Rightarrow \mathbf{b}\mathbf{=}{\mathbf{50}}^{\mathbf{°}}\end{array}$

$\begin{array}{l}\because \mathrm{a}+\mathrm{b}={180}^{°}\\ \Rightarrow \mathrm{a}+{50}^{°}={180}^{°}\\ \Rightarrow \mathbf{a}\mathbf{=}{\mathbf{130}}^{\mathbf{°}}\end{array}$

Therefore, the measures of angles $\mathrm{a}$ and $\mathrm{b}$ are respectively ${\mathbf{130}}^{\mathbf{°}}$and ${\mathbf{50}}^{\mathbf{°}}\mathbf{.}$