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Sagot :

MrRoyal

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

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