Question

Lines that appear to be tangent are tangent. O is the center of the circle. What is the value of x?60degrees

Answer 1

measured angle OCA = 60degrees;

But from the tangent theorem, measured angle OCB = 90degrees;

Thus measured angle ACB = 90 - 60 = 30 degrees.

Also, OC = OA because they represents the radius of the circle,

Thus triangle COA is an issoceles triangle.

Then measured angle OAC = 60 degrees because the base angle angles of an issoceles triangle are equal.

measured angle ABC = x = 180 - 120 - 30 because the sum of angles in a triangle is 180 degrees

Thus x = 30.