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QveST [7]
3 years ago
5

Three lines intersect at point P, as shown in the diagram below. Find the measure of

Mathematics
1 answer:
alexandr402 [8]3 years ago
4 0

Answer:

VPQ = 83°

Step-by-step explanation:

You can draw a circle around the point P, and a circle have 360°, so it means that the sum off all the angles have ro be 360°. Some of these angles have the same measure, because they're formed by the same lines segments, they are:

SPR = UPV; TPU = RPQ; TPS = VPQ

360 - SPR - UPV - RPQ - TPU = VPQ + TPS

As some of they are equal, we can just multiply they by 2:

360 - 2×SPR - 2×RPQ = 2× VPQ

360 - 2×35 - 2×62 = 2×VPQ

360 - 70 - 124 = 2×VPQ

2 VPQ = 166

VPQ = 166/2

VPQ = 83°

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