Question

Angles of a quadrilateral are ${\left(4x\right)}^{\circ },5{(x+2)}^{\circ },{(7x-20)}^{\circ }$ and $6{(x+3)}^{\circ }.$ Find each angle of the quadrilateral.

Answer 1

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

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

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

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

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

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

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

The angles of an quadrilateral are,

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

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

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

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