Question

wx and xy are tangent to ⊙v. what is m∠x? m∠x =

Explanation:

Step1: Recall tangent - radius property

A tangent to a circle is perpendicular to the radius at the point of tangency. So, $\angle VWX = 90^{\circ}$ and $\angle VYX=90^{\circ}$.

Step2: Use the sum of angles in a quadrilateral

The sum of the interior angles of a quadrilateral is $360^{\circ}$. In quadrilateral $VWXY$, we know that $\angle VWX = 90^{\circ}$, $\angle VYX = 90^{\circ}$, and $\angle WVY=145^{\circ}$. Let $\angle WXY=x$. Then, by the angle - sum formula for a quadrilateral $\angle VWX+\angle VYX+\angle WVY+\angle WXY = 360^{\circ}$.
Substitute the known values: $90^{\circ}+90^{\circ}+145^{\circ}+x = 360^{\circ}$.

Step3: Solve for $x$

First, simplify the left - hand side: $325^{\circ}+x = 360^{\circ}$.
Then, subtract $325^{\circ}$ from both sides: $x=360^{\circ}-325^{\circ}=35^{\circ}$.

Answer:

$35$