Question

Lines that appear to be tangent are tangent. O is the center of the circle. What is the value of x?

Answer 1

x = 28°

Explanation:

PQ is tangent to circle O, ∠OPQ = 90°

∠QPR = 90-59 = 31°

mOP = mOR (radius) ∠PRO = ∠OPR = 59° (isosceles triangle)

∠PRO = ∠QPR + x° (triangle exterior angle)

x = 59° - 31° = 28°

Answer 2

28

Explanation:

Neat Question.

Thanks for posting.

The straign line (horizontal) makes an isosceles triangle inside the circle. So the bottom angle of the triangle is also 59 degrees. The central angle of the interior triangle is

180 - 59 - 59 = 62.

x and the 62 degree angle are complementary -- both are in the 90 degree angle triangle made by the tangent. x + 62 = 90

x = 90 - 62 = 28