Find the measure of angle x.

Question

The figure shows a circle with several inscribed angles, with the measure of one angle given as 53°. Note that two of the line segments are perpendicular to each other.

Find the measure of angle x.

Answer 1

The triangle that has the 53 degree angle, also has a right angle, so the remaining angle in the triangle is 180 - 53 - 90 = 37 degrees. That angle intercepts the same arc as angle x, so x must have the same measure of 37 degrees.