Given an angle, draw the opposite ray of one of its sides to form a linear pair. find the measure of the angle formed by the angle bisector of the given angle and the drawn opposite ray if the measure of the given angle is: 50°, 90°, and 150°.

Let opposite ray be drawn for the base side ray of the given angle. This gives angle 180° between these two rays. Angle bisectors of the given angles 50°, 90°, and 150° make respectively half of these angles : 25° , 45° and 75° with the base ray. Then measure of the angles between the bisectors of the given angles and the drawn opposite ray are 180°-25°=155°, 180°- 45° =135° and 180°- 75° = 105° respectively.