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

Answer:m∠DRM = 45°Step-by-step explanation:∵ PSTR is a parallelogram∴ TS // RP ⇒ opposite sides∴ m∠T + m∠R = 180° ⇒ (1) (interior supplementary angles)∵ m∠T : m∠R = 1 : 3∴ m∠R = 3 m∠T ⇒ (2)- Substitute (2) in (1) ∴ m∠T + 3 m∠T = 180∴ 4 m∠T = 180∴ m∠T = 180 ÷ 4 = 45°∴ m∠R = 3 × 45 = 135°∵ m∠R = m∠S ⇒ opposite angles in a parallelogram∴ m∠S = 135°∵ RD ⊥ PS∴ m∠RDS = 90°∵ RM ⊥ ST∴ m∠RMS = 90°- In quadrilateral RMSD∵ m∠S = 135°∵ m∠RDS = 90°∵ m∠RMS = 90°∵ The sum of measure of the angles of RMSD = 360°∴ m∠DRM = 360 - ( 135 + 90 + 90) = 45°