Question - Angle Calculation Using Tangents and Congruent Segments
Solution:
The image depicts a geometric diagram involving a circle with a tangent line. The information provided in the text accompanying the image is as follows:- $$ YW $$ is a tangent to the circle at point $$ X $$.- $$ UV $$ is congruent to $$ VX $$ (which means $$ UV $$ equals $$ VX $$).- Angle $$ VXW $$ measures 50 degrees.To solve for the angle $$ UXY $$, we need to use the properties of a tangent to a circle and the fact that UV equals VX. When a line is tangent to a circle, it is perpendicular to the radius at the point of tangency. Therefore, angle $$ UXY $$, being the angle between the tangent line $$ YW $$ and the radius $$ UX $$, is a right angle or 90 degrees.Therefore, the value of angle $$ UXY $$ is 90 degrees.
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