The line TU is tangent to the circle whose center is at point S
The measure of angle U is 84 degrees
How to determine angle U?
From the question, we understand that:
- Angle STV = 84 degrees
- TU is tangent to circle S
This second highlight means that:
Angle STU = 90 degrees
And:
Angle STU = Angle STV + Angle VTU
This gives
90 = 84 + Angle VTU
Subtract 84 from both sides
Angle VTU = 6
The measure of angle U is then calculated as:
U + Angle VTU + Angle UVT = 180 ------ sum of angles in a triangle
This gives
U + 6 + 90= 180
Evaluate the sum
U + 96 = 180
Subtract 96 from both sides
U = 84
Hence, the measure of angle U is 84 degrees
Read more about tangents at:
https://brainly.com/question/6617153
