Hello!
1. To figure out the angle measurement when given two other angles from the triangle, it's important to realize that any given triangle's angles will add up to 180.
Since 25 and 52 is given to us, let's subtract 180-25-52 to get 103; this is the angle measurement of 3.
2. Assuming ray LAP is a straight line, we can conclude that 3 and 4 are supplementary angles in which they add up to 180 degrees (line).
Since we know the value for 3, we just need to subtract that from 180, the angle measurement of the line.
180-103=77; angle 4 is measured at 77 degrees
3. The angle's relationship for angles 1, 2, and 3 are correlated. Since they are a triangle, they will always add up to 180 degrees exactly; angles 2 and 3 also equal angle 4. Angle 3 and 4 are supplementary angles, which means they are two angles intersected by a ray.
4. Angles 2 and 3 from the triangle equal angle 4. This works out because those two angles add up to the angle for 4.
