Question

18. In the figure, o is the center of the circle passing through P, Q, R and S. If angle SOQ = 150°, find the values of x and y.

Answer 1

Answer:

x = 75°

y = 105°

Step-by-step explanation:

Angle subtended on the circumference of the circle is half of the angle subtended on the center of the circle.

$\therefore m\angle SRQ = \frac{1}{2} \times m\angle SOQ\\\\\therefore x = \frac{1}{2} \times 150\degree \\\\\red{\bold{\therefore x =75\degree}}$

Quadrilateral PQRS is a cyclic quadrilateral.

$\therefore m\angle R + m\angle P= 180\degree \\\\\therefore x + y = 180\degree \\\\\therefore 75\degree + y = 180\degree \\\\\therefore y = 180\degree - 75\degree \\\\\purple {\bold {\therefore y = 105\degree}}$