Points and (in this order) lie on a circle

MATHEMATICS · Subjective · CBSE · Mathematics · Circles · Circles

Problem

Points

P, Q, R,

and

S

(in this order) lie on a circle, forming quadrilateral

PQRS

. The angles of the quadrilateral are expressed as

\angle P = 2y^\circ,\; \angle Q = 90^\circ,\; \angle R = (y + 60)^\circ,\; \angle S = 90^\circ

. (i) Form an equation in

y

by using the angle relationship in

PQRS

. (ii) Solve for

y

. (iii) Calculate the exact numerical measures of

\angle P

\angle Q

\angle R

, and

\angle S

. (iv) Show that the four angles you have obtained satisfy the required angle conditions for a quadrilateral whose vertices lie on a circle.