In the figure above, line l is tangent to the circle at point P, and O is the center of the circle. What is the value of y?
Fill in the angle you know: the big angle in that triangle must be 130º. You know that’s an isosceles triangle because two sides are radii, so the the two small angles in the triangle must be congruent. That means each of them must be 25º.
Tangent lines are perpendicular to radii they intersect with, so that whole angle between the radius and the line l must be 90º. Since 25 of those degrees are in the triangle, y must equal 90 – 25 = 65º.