Ok I’ll take these one at a time
Picture 1:
You are given that two sides are congruent and you are given two angles in terms of x. You should know that all angles of a triangle must add up to 180, and if a triangle has two equal side lengths, it must have two equal angles. The equal angles will always be next to each other and the congruent sides. So because you know that all sides add up to 180, you can add all of the angles and set them equal to 180. This yields this equation:
(2x+2) + (2x+2) + (3x+1) = 180
7x + 5 = 180
7x = 175
x = 25˚
Picture 2:
This one might seem complicated being an hourglass-like shape, but just remember that all it is is 2 triangles. So lets start with the upper triangle. You know that the two sides are equal, so the two unknown angles in that triangle must also be equal. Using the fact that all three angles of any triangle will always add to 180, you can solve using the equation:
x + x + 55 = 180
2x=125
x=62.5
So angles 1 and 2 both equal 62.5
Now, the lower triangle.
If two triangles are stacked on top of each other with the same lines making up the angle, the angle must be the same. I didn’t do a very good job of explaining, but this phenomenon is known as “vertical angles” and you can search it up for a better explanation. So you know angle 3 is 55˚. The outside angle, 105, is on a straight line with angle 4, and you know that all straight lines have an angle of 180 degrees. So 180-105 will give you angle 4 which would be 75˚. Now you have two of the three angles of the bottom triangle, so because they must all add up to 180, you know that 180-75-55=50˚ so angle 5 is 50˚
Picture 3:
So once again you must apply the fact that triangles add up to 180˚ to set the sum of the three angles of the triangle equal to 180 yielding this formula:
(2x+13) + (3x) + (57) = 180
5x + 70 = 180
5x = 110
x = 22
To find y, you must remember that all straight lines are a 180 degree angle, and because you know a part of it, 57, you can do 180-57 to find y which makes y = 123