Question

How do I find the value of x here?

Answer 1

Vertical angles are equal, so the angle above 2 is also 88+x. Then, because the 2 sides of the 52° triangle are congruent, the angles beneath them are too. So you are left with the equation of that triangle being...

88 + x + 88 + x + 52 = 180
combine like terms
228 + 2x = 180
subtract 228 from both sides
2x = -48
divide both sides by 2
x = -24

Hope this helps :)