Question

What is angle V ? someone please help me

Answer 1

The angle V is
`58^(\circ)`

Step-by-step explanation:

In
`\triangle YWX`

Sum of the measure of the angles of a triangle is equal to 180 degree.

therefore,

`\angle YWX +\angle YXW+\angle WYX = 180^(\circ)` ......[1]

Substitute the values of
`\angle YWX=52^(\circ)` and
`\angle YXW=24^(\circ)` in [1]

then;

`52^(\circ)+24^(\circ)+\angle WYX = 180^(\circ)` 0r

`76^(\circ) + \angle WYX =180^(\circ)`

Simplify:-

`\angle WYX = 104^(\circ)`

Vertical opposite angle states that the angles opposite each other when two lines cross and they are always equal.

`\angle WYX` and
`\angle VYU` are vertically opposite.

therefore, by definition of vertical opposite angle;

`\angle VYU=\angle WYX = 104^(\circ)`

now, In
`\triangle VYU`

Sum of the measure of the angles of a triangle is equal to 180 degree.

therefore,

`\angle YVU +\angle YUV+\angle VYU= 180^(\circ)` ......[1]

Substitute the values of
`\angle YUV=18^(\circ)` and
`\angle VYU=104^(\circ)` in [1]

then;

`\angle YVU+18^(\circ)+104^(\circ)= 180^(\circ)` 0r

`\angle YVU+122^(\circ)=180^(\circ)`

On simplify:

`\angle YVU = 58^(\circ)`

Therefore, the angle V is, 58 degree.