Answer:
∠B = 70°
Explanation:
Let us call the angle vertically opposite ∠B as ∠C (see attached image)
Since they are vertically opposite angles it follows that ∠C = ∠B
Also ∠A and ∠C are corresponding angles. By one of the properties of two parallel lines being intersected by a transversal namely:
Corresponding Angles: Corresponding angles are formed on the same side of the transversal and in corresponding positions with respect to the parallel lines. Corresponding angles are congruent, meaning they have the same measure
This means ∠A = ∠C and since ∠C = ∠B it follows that ∠A = ∠B
Setting the expressions for ∠A and ∠B equal to each other gives
8x + 6° = 4x + 38°
Moving 4x to the left side and 6 to the right side of the above equation gives
8x - 4x = 38 - 6
4x = 32
x = 32/4 = 8
Substituting this value of x = 8 in the expression for ∠B gives:
∠B = 4(8) + 38 = 32 + 38 = 70°