Question

One of the same side angles of two parallel lines is 60 degrees greater than the other. Find the two angles.

Answer 1

Let's call the two angles A and B. We know that they are supplementary because they are same-side interior angles formed by a transversal intersecting two parallel lines. Thus, we have the equation A + B = 180 degrees.

We also know that one of the angles is 60 degrees greater than the other. Let's say angle B is the one that is 60 degrees greater than angle A. We can express this relationship as B = A + 60.

Now we can substitute B in terms of A into the first equation to solve for A:
A + (A + 60) = 180
2A + 60 = 180
2A = 120
A = 60

Now that we know A is 60 degrees, we can substitute this value back into the equation B = A + 60 to find B:
B = 60 + 60
B = 120

The two angles are 60 degrees and 120 degrees.