The measure of the angle XYZ will be [tex]\frac{1}{2} (154^0 -46^0 )[/tex] i.e. option C.
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 ST = 46°, and
Arc XZ = 154°
Now,
We know that the measure of the arc is same as that of central angle.
Now,
Join X and T,
Now,
We know that, the angle subtended at the center is the average of the measure of arc intercepted by its angle and its vertical angles.
So,
Angle XTZ [tex]=\frac{154}{2}[/tex]
And,
Angle SXT [tex]=\frac{46}{2}[/tex],
Now,
∠XTZ = ∠XYZ + ∠SXT [Exterior angle is equal to the sum of interior opposite angles]
So,
∠XYZ = ∠XTZ - ∠SXT
Now,
Substituting the values,
We get,
∠XYZ [tex]=\frac{154}{2}-\frac{46}{2}[/tex]
i.e.
∠XYZ [tex]=\frac{1}{2} (154-46)[/tex]
So, measure of angle XYZ is [tex]\frac{1}{2} (154-46)[/tex] .
Hence, we can say that the measure of the angle XYZ will be [tex]\frac{1}{2} (154^0 -46^0 )[/tex] i.e. option C.
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