Given: prst is a parallelogram m∠t: m∠r=1: 3, rd ⊥ ps , rm ⊥ st find: m∠drm

∠DRM=45°

Step-by-step explanation:

Given: PRST is a parallelogram, m∠T:m∠R=1:3, RD ⊥ PS , RM ⊥ ST.

To find: m∠DRM

Solution: Since, PRST is a parallelogram and then let m∠T=x then m∠R=3x.

From the figure, we get that m∠T+m∠R=180°(Adjacent angles)

x+3x=180°

x=45°

Therefore, m∠T=45° and m∠R=135°.

Also, in parallelogram, opposite angles are equal, therefore m∠R=m∠S=135°.

Now, We know that sum of all the angles of the parallelogram =360°, then

From the quadrilateral DRMS,

∠DRM+∠RMS+∠MSD+∠SDR=360°

∠DRM+90°+135°+90°=360°

∠DRM=360°-315°

∠DRM=45°