Geometry

Question Analysis

The main focus is to use the Outside Angle Theorem to find the measure of . We need to identify the major and minor arcs intercepted by the tangent  and the secant  and then 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:

The measure of the major arc  is . Since line ZX is a diameter (passing through the center ), the sum of the measures of arcs on either side of it is
So, the minor arc .

2. Apply the Outside Angle Theorem:

Let the major arc

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