Geometry

Question Analysis

The main focus is to use the Outside Angle Theorem to find the measure of . We know the measure of one intercepted arc and need to determine the other relevant arc measure based on the circle's properties to apply the theorem.

 

Key Concept Explanation

Outside Angle Theorem: For an angle formed by a tangent and a secant (or two secants/two tangents) from an external point to a circle, the measure of the angle is half the difference of the measures of the intercepted arcs. If the angle is , the major arc is , and the minor arc is , then .

 

Step - by - Step Solution

1. Determine the arc measures:

Since line RT is a diameter (passing through the center ), the sum of the measures of arcs on either side of it is . Given that arc , then the measure of arc .

2. Apply the Outside Angle Theorem:

Let the major arc

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