Question

Q is in the interior of angle ROS S in the interior of angle QOP. P is in the interior of angle SOR. S is in the interior of angle ROT and the measure of angle ROT is 160° the measure of angle SOT is 100° and the measure of angle ROQ to equals the measure of angle QOS equals the measure of angle POT

Answer 1

∠ROT=160°

∠SOT=100°

Now ∠SOR= ∠ROT - ∠SOT

∠ SOR = 160°-100°

∠ SOR =60°

It is given that measure of angle ROQ to equals the measure of angle QOS equals the measure of angle POT.

∠SOQ + ∠QOR = 60°

But ∠SOQ = ∠QOR

2∠SOQ=60°

∠SOQ=60°÷2

∠SOQ =30°

Also ∠POT=∠SOQ=∠ROQ=30°