What is the measure of ∠w, rounded to the nearest degree?

19°
32°
56°
71°

71°

This is an isosceles triangle because it has two sides with lengths, hence the angles opposite the equal sides are also equal, that is ∠U = ∠V.

So we can say that:

∠U = ∠V = α

∠W = β

Since the internal angles of a triangle add up to 180 degrees, then:

α + α + β = 180

2α + β = 180

β = 180 - 2α

Using the law of sine:

Therefore:

But we want to know ∠W = β, therefore:

And rounded to the nearest degree:

∠W = 71°

the answer is 62