Question

The sum of two angles of a quadrilateral is ${150}^o$ and the other angles are in the ratio $2:3$. Find the measure of two angles.

Answer 1

$\Rightarrow$ The sum of first angle second angle $={150}^o$

$\Rightarrow$ The ratio of third and fourth angle is $2:3$

$\Rightarrow$ Let third angle fourth angle be $2x$ and $3x$.

We know that in quadrilateral sum of four angles is ${360}^o.$

$\therefore$ ${150}^o+2x+3x={360}^o$

$\Rightarrow$ $5x={210}^o$

$\Rightarrow$ $x={42}^o$

$\Rightarrow$ Now, $2x=2\times {42}^o={84}^o$

$\Rightarrow$ $3x=3\times {42}^o={126}^o$

$\Rightarrow$ The measure of two angles are ${84}^o$ and ${126}^o$