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 ang
le 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
1 answer:
∠ROT=160°
∠SOT=100°
Now we calculate ∠SOR as follows: ∠SOR = ∠ROT - ∠SOT
∠SOR = 160° - 100°
∠SOR = 60°
It is stated that the angles ROQ, QOS, and POT all have the same measure.
Thus, ∠SOQ + ∠QOR = 60°
Since ∠SOQ equals ∠QOR, we can express this as:
2∠SOQ = 60°
From which we find ∠SOQ = 60° ÷ 2
∠SOQ = 30°
Also, ∠POT = ∠SOQ = ∠ROQ = 30°
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