Question

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

30.5
61
119
58

Answer 1

61

Explanation:

The line segments form a right triangle, since we know that Q is tangent to the circle (tangents form a right triangle with the radius of the circle).

We have two angles of the right triangle, 29 and 90; their sum is 29+90 = 119.

Every triangle has a sum of 180°; this leaves x as

180 - 119 = 61

Answer 2

The 29 degree angle and the angle x are complementary; that is, they sum up to 90 degrees. Thus, x + 29 = 90, and x = 61 (degrees).