Question

$a,b,c$ are three adjacent angles at a point $O$ on a line $AB$ such that their degree measures are three consecutive numbers. Find values of $a,b,c$

Answer 1

Here, $a,b,c$ are three adjacent angles at a point $O$ on a line $AB$

It is given that the measure of this three angles are consecutive numbers.

Let $a=x,b=2x$ and $c=3x$

$\Rightarrow$ $a+b+c={180}^o$

$\Rightarrow$ $x+2x+3x={180}^o$

$\Rightarrow$ $6x={180}^o$

$\Rightarrow$ $x=\frac{{180}^o}{6}$

$\Rightarrow$ $x={30}^o$

$\Rightarrow$ $a=x={30}^o$

$\Rightarrow$ $b=2x=2\left({30}^o\right)={60}^o$

$\Rightarrow$ $c=3x=3\left({30}^o\right)={90}^o$

$\therefore$ Measure of angles $a,b,c$ are ${30}^o,{60}^o$ and ${90}^o.$