Line segment XY is tangent to circle Z at point U.
If the measure of UV is 84º, what is the measure of ZYUV?

Step-by-step explanation:

The picture of the question in the attached figure

we have that

-----> given problem

so

------> by central angle

we know that

The triangle UZV is an isosceles triangle

because

ZU=ZV=radius

so

-----> bases angle of the isosceles triangle

Remember that

The sum of the internal angles of any triangle must be equal to 180 degrees

so

substitute and solve for m<ZUV

Find the measure of angle YUV

we have that

------> by complementary angles

substitute the given value and solve for m<YUV

its a straight line parallel to the time axis

3 is greater then both of those numbers