Question

What is the measure of XY?

Answer 1

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,

$\angle YVZ+\angle UVZ=180^\circ\\\\90^\circ+\angle UVZ=180^\circ\\\\\angle UVZ=180^\circ-90^\circ\\\\\angle UVZ=90^\circ$

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,

$\angle YVZ=\frac{UZ+XY}{2}\\\\90^\circ=\frac{UZ+XY}{2}\\\\90\times 2=UZ+XY\\\\180^\circ=127^\circ+XY\\\\180^\circ-127^\circ=XY\\\\XY=53^\circ$

Hence, the measure of XY is 53°.

Therefore, Option 'B' is correct.