Question

PQRS is a cyclic quadrilateral $\angle P=3x,\angle Q=y,\angle R=x,\angle S=5y$. Find x and y.

• A. $x={30}^{\circ },y={45}^{\circ }$
• B. $x={30}^{\circ },y={30}^{\circ }$
• C. $x={45}^{\circ },y={30}^{\circ }$
• D. $x={45}^{\circ },y={45}^{\circ }$

Answer 1

The correct option is C

$x={45}^{\circ },y={30}^{\circ }$

Since, PQRS is a cyclic quadrilateral.

So,
$\begin{array}{ccc}5y+y=180& \text{and},& 3x+x=180\\ 6y=180& & 4x=180\\ y={30}^{\circ }& & x=\frac{180}{4}\\ & & x={45}^{\circ }\end{array}$