Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
Measure of UZ = 127°
∠YVZ=∠XVZ=90°
Now, we know that ∠YVZ and ∠UVZ are linear pair.
so, it becomes,
[tex]\angle YVZ+\angle UVZ=180^\circ\\\\90^\circ+\angle UVZ=180^\circ\\\\\angle UVZ=180^\circ-90^\circ\\\\\angle UVZ=90^\circ[/tex]
So, now we have the measure of angle 90° and one intercepted arc which is equal to 127°.
As we know that the measure of angle is half the sum of the intercepted arcs,
so, it becomes,
[tex]\angle YVZ=\frac{UZ+XY}{2}\\\\90^\circ=\frac{UZ+XY}{2}\\\\90\times 2=UZ+XY\\\\180^\circ=127^\circ+XY\\\\180^\circ-127^\circ=XY\\\\XY=53^\circ[/tex]
Hence, the measure of XY is 53°.
Therefore, Option 'B' is correct.
