Question

The measures of angle of $a$ $\square$ PQRS are $3x,4x,5x$ and $6x$ respectively find $x$ and the measures of $\angle$P.

Answer 1

$\angle P=3x,\angle Q=4x,\angle R=5x$ and $\angle S=6x$.

We know that, the sum of the measure of four angles of a quadrilateral is ${360}^o.$

$\therefore$ $\angle P+\angle Q+\angle R+\angle S={360}^o.$

$\Rightarrow$ $3x+4x+5x+6x={360}^o$

$\Rightarrow$ $18x={360}^o$

$\Rightarrow$ $x=\frac{{360}^o}{18}$

$\therefore$ $x={20}^o$

$\Rightarrow$ $\angle P=3x=3\times {20}^o={60}^o$