A ray is drawn from the apex of the angle, perpendicular to its bisector

A ray is drawn from the apex of the angle, perpendicular to its bisector and forming an angle of 160 degrees with the side of this angle. Find the value of this angle.

We take x as the value of the angle, then

x / 2 is the angle between the side of the angle and the bisector;

90 + x / 2 – angle between the ray and the side, equal to 160 according to the problem statement. We get the equation:

90 + x / 2 = 160;

x / 2 = 160 – 90 = 70;

x = 140.

Answer: the desired angle is 140 degrees.