Geometry

Question Analysis

The main focus is using the perpendicular bisector of to find the length of . We'll first find the value of based on the equal - length relationship of and from the perpendicular bisector theorem, and then calculate .

 

Key Concept Explanation

The perpendicular bisector theorem states that if a point lies on the perpendicular bisector of a line segment, it is equidistant from the endpoints of that line segment. Here, since is the perpendicular bisector of (shown by the right - angle at and equal - length markings on and ), we have .

 

Step-by-Step Solution

1. Set up the equation:

Because according to the perpendicular bisector theorem, we get .

2. Solve for :

Subtract from both sides: , which simplifies to .

Add 89 to both sides: , so

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