Question

in the fig PQ=PR nd SP is parallel to QR.if angle SPQ =75 find angle QPR

Answer 1

Given that PQ = PR

angle SPQ =60°

"If any two lines of equal length intersects any two parallel lines, then the angle made with parallels by those two lines are equal, starts from a point on any of those two parallels"
which represents angle APR = angle SPQ

to get the angle at P 75°+angle P + 75° = 180( angle made by line is 180°

angle P = 30°

Any doubts comment ;)

Answer 2

Given- PQ=PR
Angle SPQ=75°

TO FIND- angle QPR

angle PQR=75° (alternate angle)

angle PRQ = 75° (opposite angle of equal side is equal)

Angle QPR+ angle PQR+ angle PRQ=180°( angle sum property)

QPR + 75 + 75 = 180
QPR + 150 = 180
QPR = 180-150
QPR=30°
Therefore angle QPR = 30°