In a circle, and are in that order on the circumference forming a quadrilateral . The…

MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles

Problem

In a circle,

W,X,Y

and

Z

are in that order on the circumference forming a quadrilateral

WXYZ

. The four interior angles are expressed as

\angle W = (4x+10)^{\circ},\; \angle X = (3y-5)^{\circ},\; \angle Y = (2x+15)^{\circ},\; \angle Z = (5y-55)^{\circ}

. (i) Set up two independent linear equations in

x

and

y

using the angle relationships in a cyclic quadrilateral. (ii) Solve the system of equations to find the values of

x

and

y

. (iii) Using these values, compute the numerical measures of all four angles of

WXYZ

and verify that your answers satisfy the required angle relationships.