Question

For this figure, what is the value of x?

Answer 1

The angles inside a triangle always add up to 180 degrees.
The whole thing is one big triangle made of two smaller ones.

28 + 58 + 77 + x = 180
163 + x = 180
x = 180 - 163
x = 17

Answer 2

The sum of the interior angles of this triangle must be 180 degrees.

Adding them up:  [28]   +   [58 + 77]   +   [x] = 180

Solving for x:  28+ 135 + x = 180

                                        x = 180 - (28+35) = 117 (degrees)    (answer)