Question

The ratio between three angles of a quadrilateral is $7:11:13$ respectively, the value of the fourth angle of the quadrilateral is ${112}^o$. what is the difference between the largest and smallest angles of the quadrilateral ?

Answer 1

Let $7x,11x,13x$ be the these angles of a quadrilateral

Given $4^{th}$ angle = ${112}^{\circ }$

By angle sum property,

$7x+11x+13x+{112}^{\circ }={360}^{\circ }$

$31x={360}^{\circ }-{112}^{\circ }={248}^{\circ }$

$x=\frac{{248}^{\circ }}{31}=8^{\circ }$

$\therefore 7x=7\times 8^{\circ }={56}^{\circ }11x=11\times 8^{\circ }={88}^{\circ }$

$13x=13\times 8={104}^{\circ }$

Largets angle = ${112}^{\circ }$

smallest angle = ${56}^{\circ }$

Difference = ${112}^{\circ }-{56}^{\circ }={56}^{\circ }$