Question

In quadrilateral PQRS, $\angle P:\angle Q:\angle R:\angle S=3:4:6:7.$ Calculate each angle of the quadrilateral and then prove that PQ and SR are parallel to each other.

Answer 1

Let the angles be 3x,4x,6x,7x
3x+4x+6x+7x = 3600
$20x={360}^{\circ }x=\frac{360}{20}=18$
$\angle P=3\times 8=5\angle Q=4\times 18=72\angle R=6\times 8={108}^{\circ }$
$\angle s=7\times 18=126$

$\angle P+\angle s={180}^{\circ }$
Therefore, PQ is parallel to RS
$\angle P+\angle a\ne {180}^{\circ }$ therefore PS is not parallel to RQ
therefore PQRS is a trapezium.