Look at the picture.
∠2 and ∠3 are Corresponding Angles. j || k, thereofre m∠2 = m∠3.
∠1 and ∠3 are supplementary angles, therefore m∠1 + m∠3 = 108°.
m∠1 = 10x + 4, m∠2 = m∠3 = 4x - 6. Therefore we have the equation:
(10x + 4) + (4x - 6) = 180
(10x + 4x) + (4 - 6) = 180
14x - 2 = 180 add 2 to both sides
14x = 182 divide both sides by 14
x = 13
10x + 4 = 10(13) + 4 = 130 + 4 = 134
4x - 6 = 4(13) - 6 = 52 - 6 = 46
Answer x = 13, m∠1 = 134°, m∠2 = 46°