Question

in the given figure,∆QPS ~∆SRQ find the value of x ,
angel PQS
angel PSR​

Answer 1

Answer:

:· X = 51

:· angle PQS = 30°

:· angle PSR = 60°

Step-by-step explanation:

angle P = 2x + 18

but,

angle P and angle R is corresponding angle of similar triangle

:· angle P = 2x + 18 = 120°

__2x = 120 - 18

__ x = 102/2

__ x = 51° ---------------------------- ( 1 )

angle QSR = 180 - angle SQR - Angle QRS

= 180 -30 -120 = 30 ° ---- ( properties of triangle )

:· angle QSR = 30° ------------------------ ( 2 )

angle PSR = Angle PSQ + QSR

But,

angle PSQ = angle QSR ------- ( Corresponding angles of similar triangles )

:· Angle PSR = 2 × QSR

= 2 × 30 -------- { by equations (2) }

= 60°

:· X = 51

:· angle PQS = 30°

:· angle PSR = 60° --------- ( 3 )