Question

If segment ac and segment bc are tangent to circle o find the value of x

Answer 1

x = 130°

Explanation:

At the points of Tangency, A and B, the angle formed are equal to 90° based on the tangent theorem.

Therefore, m<A and m<B both have a degree measure of 90° each.

Thus, the sum of the interior angles of quadrilateral AOBC = 360° (sum of interior angles of a quadrilateral).

Therefore:

x + m<A + m<B + m<C = 360°

x + 90 + 90 + 50 = 360 (substitution)

x + 230 = 360

x = 360 - 230 (subtraction property of equality)

x = 130°