Question

Given: PSTR is a parallelogram m∠T:m∠R=1:3, RD ⊥ PS , RM ⊥ ST Find: m∠DRM

Answer 1

As we know the sum of consecutive angles of a parallelogram is 180 degrees, we can calculate them. 1k+3k=180 and k=45. It is the measure of the angle R (in the picture, angle B). Since MR is perpendicular, we can find angle MRT (in the picture it is BCF). And it is 45 degree according to the theorem about the sum of all angles of a triangle. From here, we can say that ∠DRM=135-45=90 degree.