ok, so first know that the angle x and the angle oposite it (next to 52 degrees) are the same
and the 2 other angles in the triangle with the 52 degre angle are the same measure
there are several ways to solve, but all of them require us to find all the angles
so
notice that 2 angles in the triangle are the same measure
so
and also all angles add to 180 in a triangle
so ?+?+52=180
2?+52=180
minus 52 both sides
2?=128
divide both sides by 2
?=64
now we do another thing
consider the bigger trignalg
it has angles of ?, 52+x, and x (the double angle measure thing means same)
so
they add to 180
and ?=64
64+52+x+x=180
116+2x=180
minus 116 both sides
2x=64
divide both sides by 2
x=32
