geometry
posted by crystal .
in triangle PQR,line segment PQ is = and congruent to line segment QR. if m<p = 4x + 50, m<Q =2x + 60 and m<R = 14x + 30, find the measure of each angle.

You have conflicting information.
First of all, the 3 angles must add up to 180°, so
4x+50 + 2x+60 + 14x + 30 = 180
20x = 40
x = 2
and the 3 angles would be 58°, 64° , and 42°.
BUT, in the first sentence you said that PQ = QR, making it isosceles.
Contradiction!
Two of the angles would have to be equal.