Questions: T U is tangent to circle S. What is m angle S? m angle S=

Transcript text: $\overleftrightarrow{T U}$ is tangent to $\odot S$. What is $m \angle S$ ? \[ m \angle S= \]

Solution

Solution Steps

Step 1: Analyze the given information

Line TU is tangent to circle S at point T. This means that angle STU is a right angle, measuring 90 degrees. Triangle STU is a right triangle. We are given that angle SUT measures 42 degrees.

Step 2: Use the properties of triangles

The sum of the angles in any triangle is 180 degrees. In triangle STU, we know two angles: angle STU (90 degrees) and angle SUT (42 degrees). We can find the measure of angle S using this property.

Step 3: Calculate angle S

Angle S = 180 - (angle STU + angle SUT) = 180 - (90 + 42) = 180 - 132 = 48 degrees.