Question

pq is tangent to circle l. what is the value of x?

Explanation:

Step1: Recall tangent - radius property

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

Step2: Use angle - sum property of a triangle

In $\triangle LPQ$, we know that the sum of the interior angles of a triangle is $180^{\circ}$. Let $\angle PLQ = 25^{\circ}$, $\angle LPQ=90^{\circ}$, and $\angle PQL=x$. Then, by the angle - sum property of a triangle $\angle PLQ+\angle LPQ+\angle PQL = 180^{\circ}$.
Substitute the known values: $25^{\circ}+90^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

First, simplify the left - hand side: $115^{\circ}+x = 180^{\circ}$. Then, subtract $115^{\circ}$ from both sides: $x=180^{\circ}- 115^{\circ}=65^{\circ}$.

Answer:

$65$