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°
