Question

Line segment XY is tangent to circle Z at point U. If the measure of is 84°, what is the measure of ? 42° 84° 96° 168°

Answer 1

a 42

Explanation:

Answer 2

The measure of angle YUV is equal to
`m<YUV=42\°`

Explanation:

see the attached figure to better understand the problem

we have that

`arc\ UV=84\°` -----> given problem

so

`m<UZV=84\°` ------> by central angle

we know that

The triangle UZV is an isosceles triangle

because

`ZU=ZV=radius`

so

`m<ZUV=m<ZVU` -----> bases angle of the isosceles triangle

Remember that

The sum of the internal angles of a triangle is equal to
`180\°`

so

`m<ZUV+m<ZVU+m<UZV=180\°`

`2m<ZUV+m<UZV=180\°`

substitute and solve for m<ZUV

`2m<ZUV+84\°=180\°`

`m<ZUV=(180\°-84\°)/2=48\°`

`m<ZUV+m<YUV=90\°` ------> by complementary angles

solve for m<YUZ

`48\°+m<YUV=90\°`

`m<YUV=90\°-48\°=42\°`