Question

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°.

Answer 1

For 50°, answer is 65° For 90°, answer is 45° For 150°, answer is 15° A linear pair of angles adds up to 180° by definition. So the new angle drawn by the ray will have an angle of 180°-a where a is the measure of the original angle. And the bisector of that new angle will be (180°-a)/2. So with that in mind, let's calculate the new measures of the described construction. 50°: (18° - 50°)/2 = 130°/2 = 65° 90°: (180° - 90°)/2 = 90°/2 = 45° 150°: (180° - 150°)/2 = 30°/2 =15°