Question

The answer to this problem. My app shut out while my tutor was helping

Answer 1

Let's draw first the triangle being described to better understand the scenario:

The triangle appears to be an isosceles triangle, the two angles opposite to the equal sides are congruent to each other. That means it has two congruent base angles and this is called an isosceles triangle base angle theorem.

In other words, ∠U and ∠W must be equal.

`\angle U\text{ = }\angle W`

Also, recall that one property of a triangle, the sum of all of its interior angles is equal to 180°.

`\angle1\text{ + }\angle2\text{ + }\angle3=180^(\circ)`

Using those properties of triangles, let's find the measure of ∠V.

∠1 = ∠U = 75°

∠2 = ∠V

∠3 = ∠W

∠U = ∠W

∠1 + ∠2 + ∠3 = 180°

We get,

`\angle1+\angle2+\angle3=180\degree`
`\angle U+\angle V+\angle W=180\degree`
`\angle U+\angle V+\angle U=180\degree`
`75^(\circ)+\angle V+75^(\circ)=180\degree`
`\angle V+150^(\circ)=180\degree`
`\angle V=180\degree\text{ - }150^(\circ)`
`\angle V=30^(\circ)`

Therefore, the measure of ∠V = 30°