Answers are
Angle A = 46
Angle B = 154
Step by step
Angle A is a corresponding angle with 4u + 26, so it is the same.
Angle A is a supplementary angle with
22u + 24, so their sum is 180 degrees on the straight angle. See the red angles on the attachment.
We can substitute A with 4u + 26 and solve
4u + 26 + 22u + 24 = 180
Combine
26u + 50 = 180
Subtract 50 from both sides to isolate variable
26u + 50 - 50 = 180 -50
26u = 130
Divide both sides by 26 to solve
26/26 u = 130/26
u = 5
A = 4u + 26
Substitute 5 for u
A = (4) (5) + 26
A = 20 + 26
A = 46
Angle B
We know the two blue angles on the attachment are corresponding angles so they are the same (7w + 5)
We also know angle (w + 23) is a vertical angle to (7w + 5)
We can solve
w + 23 = 7w + 5
Subtract w from both sides to isolate w
w - w + 23 = 7w -w + 5
23 = 6w + 5
Subtract 5 from both sides to isolate constant
23 - 5 = 6w +5 - 5
18 = 6w
Divide both sides by 6 to solve for w
18/6 = 6/6 w
w = 3
Now we can find either angle value
w + 23 = 7w + 5
sub 3 for w
(3) + 23 + (7)(3) + 5
26 = 26
Both vertical angles are 26
Now we know that the straight angle sum will equal 180, so
26 + B = 180
subtract 26 from both sides to solve
26 - 26 + B = 180 - 26
B = 154