Answer:
The angle V is [tex]58^{\circ}[/tex]
Explanation:
In [tex]\triangle YWX [/tex]
Sum of the measure of the angles of a triangle is equal to 180 degree.
therefore,
[tex]\angle YWX +\angle YXW+\angle WYX = 180^{\circ}[/tex] ......[1]
Substitute the values of [tex]\angle YWX=52^{\circ}[/tex] and [tex]\angle YXW=24^{\circ}[/tex] in [1]
then;
[tex]52^{\circ}+24^{\circ}+\angle WYX = 180^{\circ}[/tex] 0r
[tex]76^{\circ} + \angle WYX =180^{\circ}[/tex]
Simplify:-
[tex]\angle WYX = 104^{\circ}[/tex]
Vertical opposite angle states that the angles opposite each other when two lines cross and they are always equal.
[tex]\angle WYX [/tex] and [tex]\angle VYU [/tex] are vertically opposite.
therefore, by definition of vertical opposite angle;
[tex]\angle VYU=\angle WYX = 104^{\circ}[/tex]
now, In [tex]\triangle VYU [/tex]
Sum of the measure of the angles of a triangle is equal to 180 degree.
therefore,
[tex]\angle YVU +\angle YUV+\angle VYU= 180^{\circ}[/tex] ......[1]
Substitute the values of [tex]\angle YUV=18^{\circ}[/tex] and [tex]\angle VYU=104^{\circ}[/tex] in [1]
then;
[tex]\angle YVU+18^{\circ}+104^{\circ}= 180^{\circ}[/tex] 0r
[tex]\angle YVU+122^{\circ}=180^{\circ}[/tex]
On simplify:
[tex]\angle YVU = 58^{\circ}[/tex]
Therefore, the angle V is, 58 degree.
