Really lovely.
Looking at the angles y and (2y-6), they are opposite interior angles of two parallel lines. Their sum is 180.
y + (2y -6) = 180
3y - 6 = 180
3y = 180 + 6
3y = 186 Divide both sides by 3.
y = 186/3 = 62. y = 62.
y + w = 180 sum of angles on a straight line.
62 + w = 180
w = 180 -62 = 128
w = 128.
Looking at the triangle:
w + z + 30 = 180 Sum of angles in a triangle, substituting w.
128 + z + 30 = 180
z + 158 = 180
z = 180 - 158 = 22.
z = 22.
x = z Alternate angles between parallel lines are equal.
but z = 22.
Therefore, x = 22.
Cheers.
