Find the missing angles for 1 and 2

In picture 1 we got a right triangle on the left. Two given angles are the 90° and a 30°. When we calculate the remaining angle we get:




The bottom right angle of the right triangle is 60°.

At the bottom, we see a straight line with 3 angles on it. Because that angles made up a straight line, we know their sum is equal to 180°. When we convert that into an equation:

Simplify:



We learned that the left bottom angle of the triangle on the right equals 50°.

At the triangle on the right we have two angles known: 50°, and 85°. We can find the third angle by setting their sum equal to 180:

Simplify:



For picture 2, we know that those two triangles have congruent angles in the middle. The two angles in the middle are what we call 'vertical' angles.

Because their one angle is equal, their remaining two angles' sum needs to be equal to each other. So

When we simplify this:



So, the ? is 29.

(I used x and y but I made them up)