Question

The angles of a quadrilateral $PQRS$, $\angle P,\angle Q,\angle Rand\angle S$ are $x°,(x-10)°,(x+30)°and2x°$
respectively. Sort the angles in increasing order of magnitude.

• A. $\angle Q$
• B. $\angle P$
• C. $\angle R$
• D. $\angle S$

Answer 1

We know that the sum of all angles in a quadrilateral is 360${}^{\circ }$.
Then, $x^{\circ }+(x-10{)}^{\circ }+(x+30{)}^{\circ }+(2x{)}^{\circ }={360}^{\circ }$
$5x^{\circ }+{20}^{\circ }={360}^{\circ }$
$x=\frac{340}{5}={68}^{\circ }$
The angles P, Q, R and S are ${68}^{\circ },{68}^{\circ }-{10}^{\circ },{68}^{\circ }+{30}^{\circ },2\times {68}^{\circ }$
$i.e.{68}^{\circ },{58}^{\circ },{98}^{\circ },{136}^{\circ }$ respectively.
$\therefore$ Q, P, R, S are the angles in increasing order.