Question

PQRS is cyclic and Q-R-T , if angle QPS=110° angle QRS=X and angle SRT=Y , then find Value of X and Y .​

Answer 1

Answer:

QPS=110°(Given)

therefore QPS+QRS=180° (In a cyclic quadrilateral opposite angles add up to 180°)

110°+QRS=180°

QRS=180°-110°

QRS=70°

Now for SRT

SRT=QPS (In a cyclic quadrilateral exterior angle is equal to interior opposite angle)

therefore SRT=110°

Answer 2

Given : Quadrilateral PQRS is cyclic and Q-R-T.

Angle QPS= 110, angle QRS = X and angle SRT=Y

To find  : x and y

Solution:

In  cyclic  Quadrilateral sum of opposite angles = 180°

=> ∠QPS + QRS  = 180°

∠QPS = 110°   Given

∠QPS = x   Given

=> 110° + x =  180°

=> x = 70°

∠QRS + ∠SRT = 180°   Linear pair ∵ Q-R-T

=>  70° +  ∠SRT = 180°

=> ∠SRT = 110°

=> y =  110°

x = 70°  and y =  110°

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