Given:  In rt
bisects 
Find: 

The measure of angle
Given:
In right
Definition:
Angle bisector bisects the angle in half.
The sum of the measures of interior angles of a triangle is
If two lines intersect each other than the vertical angle formed are congruent to each other and their measures are same.
Calculation:
Consider the given figure.
Figure
Consider the right triangle
Substitute
Since, the angle bisector bisects the angle in half, then from the figure
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