Three lines intersect at point , as shown in the diagram below. Find the measure of ∠VPQ. SHOW ALL WORK.

83

Step-by-step explanation:

First of all, notice that VPS is a straight line meaning angles that lie on it will have a sum of 180. We know length of SPR=35, RPQ=62 (vert.opps.<s) as it lies vertically opposite to TPU. So now we know 2 angles, we can easily find out 3rd angle. But first we have to assume it as x. We make an equation= 62+35+x=180, 97+x=180,x=180-97, x=83, so angle VPQ equals 83.

the answer is 40.

proof: