Geometry

Question Analysis

The main focus is on using the property that when a diameter is perpendicular to a chord, the arcs on either side of the diameter are equal. We'll set up an equation based on the given arc - measure expressions to find the value of .

 

Key Concept Explanation

When a diameter is perpendicular to a chord, it divides the associated arcs into two equal - measure parts. This allows us to equate the expressions for the arc measures to solve for the unknown variable.

 

Step - by - Step Solution

1. Since the diameter is perpendicular to the chord, the two arcs are equal. So, we set up the equation:

.

2. Move the  terms to one side and the constant terms to the other side:

Subtract  from both sides: , which simplifies to

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