Question

-50 Points-
If segment AC and segment BC are tangent to circle O, find the value of x.

Answer 1

AOB ( x) + ACB = 180

AOB (x) + 10 = 180

x = 180-10

x = 170

Answer 2

x = 170 deg

Explanation:

A tangent to a circle is perpendicular to the radius of the circle at the point of tangency. That means that in quadrilateral AOBC, angles A and B are right angles and measure 90 deg.

The sum of the measures of the angles of an n-sided polygon is

(n - 2)180 deg

In this case, n = 4, so

(4 - 2)180 deg = 360 deg

m<A + m<O + m<B + m<C = 360

90 + x + 90 + 10 = 360

x + 190 = 360

x = 170

Answer: 170 deg