The measure of the angle XYZ will be [tex]72^0[/tex] .
What is angle ?
Angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
We have,
Arc [tex]XYV = 64^0[/tex]
Arc [tex]ZYW = 152^0[/tex]
Now,
We know that the measure of the arc is same as that of central angle..
So from the above mentioned statement,
We get,
[tex]\angle XYV =64^0[/tex] and,
[tex]\angle ZYW =152^0[/tex]
From the given figure it can be assumed that,
[tex]\angle VYW=\angle XYZ[/tex]
Because they are vertically opposite angles.
So,
Let [tex]\angle VYW=\angle XYZ=x[/tex]
And,
Sum of all angles of circle is equals to [tex]360^0[/tex] .
i.e. [tex]\angle VYW+ \angle XYZ + \angle XYV + \angle ZYW =360^0[/tex]
⇒[tex]x+x+64+152=360[/tex]
[tex]2x=360-216[/tex]
[tex]2x=144[/tex]
[tex]x=72^0[/tex]
So, measure of angle XYZ is [tex]72^0[/tex] .
Hence, we can say that the measure of the angle XYZ will be [tex]72^0[/tex] .
To know more about angle click here
https://brainly.com/question/23247585
#SPJ3
