Question

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

Answer 1

Hello!

A triangle is 180 degrees, and you are given one of the angles, which is ∠P = 26 degrees.

Angle Q is a right angle, and this triangle is therefore a right triangle, so one angle has to be 90 degrees, and the other two angles are acute.

So we can create a simple equation:

m∠P + m∠Q + m∠x = 180 degrees

26 + 90 + m∠x = 180

116 + m∠x = 180

-116 - 116

m∠x = 64 degrees.

The measure of angle x is equal to 64 degrees, which is the fourth choice.