Question

Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x.

m<O = 135
(See picture down below)

a) 45

b) 315

c) 270

d) 67.5

Answer 1

Draw an imaginary line from the vertex of angle x to the center of the circle.
This divides the 4-sided polygon into two right triangles. For example, the upper right triangle has an acute angle whose measure is 135 degrees / 2, or 67.5 degrees, and the another acute angle whose measure is x/2.

x/2 and 67.5 degrees are complementary angles, so x/2 + 67.5 deg = 90 deg. Thus, x/2 = 22.5 deg, and so x = 45 deg. (answer)