Question

Line segment XY is tangent to circle Z at point U.

Answer 1

Answer:

42

Step-by-step explanation:

hope this helps

Answer 2

Answer:

$m\angle YUV=42\°$

Step-by-step explanation:

The picture of the question in the attached figure

we have that

$arc\ UV=84\°$ -----> given problem

so

$m\angle UZV=84\°$------> by central angle

we know that

The triangle UZV is an isosceles triangle

because

ZU=ZV=radius

so

$m\angle ZUV=m\angle ZVU$ -----> bases angle of the isosceles triangle

Remember that

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

so

$m\angle ZUV+m\angle ZVU+m\angle UZV=180\°\\2m\angle ZUV+m\angle UZV=180\°$

substitute and solve for m<ZUV

$2m\angle ZUV+84\°=180\°\\m\angle ZUV=(180\°-84\°)/2=48\°$

Find the measure of angle YUV

we have that

$m\angle ZUV+m\angle YUV=90\°$ ------> by complementary angles

substitute the given value and solve for m<YUV

$48\°+m\angle YUV=90\°\\m\angle YUV=90\°-48\°=42\°$