Question

PLEASE HELP! 

Answer 1

In order to answer this question you have to know two things:

-- "Complementary" angles means that they add up to 90 degrees.

-- "Supplementary" angles means that they add up to 180 degrees.

If you know these two things, then this question should be easy for you.
If you don't know them, then there is no way.
Now that I've told you these two things, you have everything you need
   with which to answer the question, and I should not have to go through
   the rest of the solution for you.
But you have been so generous with your valuable points, and you do have
   an Irish name on March 17, so I guess I should follow it through to the end.

I'd like to dedicate this solution to the memory of the late Sir Robert Briscoe,
the first Jewish Lord Mayor of Dublin.  Go raibh maith agat.

Part a).
Angle 'a' is 52 degrees.
Angles 'a' and 'b' are complementary angles.
That means they add up to 90 degrees.

                                          a + b = 90

                                        52 + b = 90

Subtract 52 from each side:    b = (90 - 52)  =  38 degrees


Part B).
Angle 'A' is still 52 degrees.
Angles 'A' and 'X' are supplementary angles.
That means they add up to 180 degrees.

                                          A + X = 180

                                         52 + X = 180

Subtract 52 from each side:     X = (180 - 52)  =  128 degrees