Question

In the given figure PS is an angle bisector of angle P and PM is perpendicular to QR. Find angle MPS.
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Answer 1

Answer:

in tri. PQM

angle P+angle Q+angle M=180°

(by angle sum property of triangle)

P+80 degree+90 degree=180 degree

angle P+170 degree =180 degree

angle P =10 degree

In triangle PMR,

angle P+angle M+angle R=180°

angle P + 90°+ 50°=180°

angle P=40°

angle MPS =angle MPR - angle QPM

angle MPS =40°-10°

angle MPS =30°