There are many great ways to combine geometry and algebra. These problems aren't any of them. Ugh.
1. The three triangle angles add to 180 so the sum of the two given ones 5x+45 are supplementary to the third, as is the given 6x + 30. So
5x + 45 = 6x + 30
15 = x
Answer: 15
Note: not 15°, the units were already built into the expression and shouldn't be repeated.
2. I wish they would label these better.
The middle triangle is equilateral so the unlabled angle between 40 and x must be 60 degrees.
We have parallel lines, and a transversal, so our 60 degree angle is alternate interior to y, so y = 60 (not 60° because the degree sign is not part of y, it's external).
Similarly, the unlabeled angle all the way to the right is 40°, corresponding angles to a different traversal of the parallel lines.
so x + y + 40 = 180, x = 140 - 60 = 80
Answer: x = 80, y = 60, middle triangle is equilateral
3.
We have two isosceles triangles, so
3x - 6 = 2y = 14 - 2x
3x - 6 = 14 - 2x
5x = 20
x = 4
2y = 14 - 2x = 14 - 8 = 6
y = 3
Answer: x = 4, y = 3
We're only allowed to do three. Merry Christmas.