Question

in parallelogram PQRS ,find angle RPS, angle ORS and angle RSQ​

Answer 1

Answer:

sorry couldn't give the answer something is wrong with the question

Answer 2

Answer: =∠RPS 45°

                 ∠ORS= 75°

                 ∠RSQ=35°

Step-by-step explanation:

PQRS is parallelogram

Now,

∠ROS + ∠SOP = 180°     [Linear pair angle]

   ∠ROS + 110°= 180°

    ∠ ROS = 180°-110°

  ∠ROS = 70°  

∠PQR = ∠RSQ = 35° [ alternate angle]

∠RSQ = 35°

In Δ ROS,

∠ROS + ∠RSQ + ∠ORS = 180°  [ sum of angles of Δ is 180°]

35° + 70° + ∠ORS = 180°

105° + ∠ORS = 180°

∠ORS = 180°-105°

∠ORS = 75°

Now  ∠POS = ∠QOR = 110° [ vertically opposite angle are equal]

So, in Δ QOR,

∠RQO + ∠QOR + ∠ORQ = 180°  [ again sum of angles of Δ is 180°]

25° + 110° + ∠ORQ = 180°

135° + ∠ORQ = 180°

∠ORQ = 45°

Now as we know,

∠QRP = ∠RPS = 45° [ Alternate angles]

so, ∠ RPS = 45°