First picture:
When two lines intersect, they form 4 angles. Each 2 vertically opposed angles, are equal.
The sum of 2 angles is 114. We suppose they are vertically opposed, which means that each angle is 114/2 = 57 degrees.
Now the 4 angles of 2 intersect lines form a 360 degrees angle. Which means that the sum of the 2 other angles is 360 - 114 = 246 degrees.
Same thing, we divide that angle in 2 and we get 246/2 = 123. Which means that the other 2 angles are 123 degrees each.
So the sum of all the angles are 57, 57, 123 and 123.
Second Picture:
By hypothesis, we know that the angle is 172 degrees. The angle bisector divides an angle in 2 equal angles. So both angles, in this case, will be 172/2 = 86 degrees.
So the measure of an angle formed by the angle bisector of a given angle (172 degrees) and one of its sides is, in this case, 86 degrees.
Hope this helps! :)
