Question

Draw an angle and then draw the opposite ray to one of its sides to form a linear pair. Find the measure of the angle formed by the angle bisector of the original angle and the opposite ray if the original angle bisector measures 50 degrees, 90 degrees, and 150 degrees If the angle equals 50 degrees then the measurement of the required angle is

Answer 1

1. 155 degree

2. 135 degree

3. 105 degree

Explanation:

1. Let the original angle is 50 degree, the opposite angle which forms a linear pair is 180 - 50 = 130 degree.

Now the angle bisector is 25 degree from the original ray , the angle between the bisector and the opposite ray is 130 + 25 = 155 degree.

2. Let the original angle is 90 degree, the opposite angle which forms a linear pair is 180 - 90 = 90 degree.

Now the angle bisector is 45 degree from the original ray , the angle between the bisector and the opposite ray is 90 + 45 = 135 degree.

3. Let the original angle is 150 degree, the opposite angle which forms a linear pair is 180 - 150 = 30 degree.

Now the angle bisector is 75 degree from the original ray , the angle between the bisector and the opposite ray is 30 + 75 = 105 degree.