Question

Angles of a quadrilateral are $(4x{)}^{\circ },5(x+2{)}^{\circ },(7x-20{)}^{\circ }$ and $6(x+3{)}^{\circ }$.
(i) Find the value of $x$ (in degrees).
(ii) Each angle of the quadrilateral

Answer 1

The given angles of a quadrilateral are $\left(4x{0}^o.5\right(x+2{)}^o,(7x-20{)}^o$ and $6(x+3{)}^o.$

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

$\therefore$ $4x+5(x+2)+7x-20+6(x+3)={360}^o$

$\Rightarrow$ $4x+5x+{10}^o+7x-{20}^o+6x+{18}^o={360}^o.$

$\Rightarrow$ $22x+8^o={360}^o$

$\Rightarrow$ $22x={352}^o$

$\Rightarrow$ $x=\frac{{352}^o}{22}$

$\therefore$ $x={16}^o$

Now, we are going to find each angle of the quadrilateral.

$\Rightarrow$ $(4x{)}^o=4\times {16}^o={64}^o$

$\Rightarrow$ $5(x+2{)}^o=5({16}^o+2^o)=5({18}^o)={90}^o$

$\Rightarrow$ $(7x-20{)}^o=(7\times {16}^o-20{)}^o={92}^o$

$\Rightarrow$ $6(x+3{)}^o=6({16}^o+3^o)=6({19}^o)={114}^o$

$\therefore$ Measure of the angles of quadrilateral are ${64}^o,{90}^o,{92}^o$ and ${114}^o.$