Answer: 57 degrees
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Step-by-step explanation:
A is complementary to B, so A+B = 90. Similarly, B+C = 90 (since C is complementary to B).
A+B = 90
(3x+y)+(x+4y+2) = 90 ... substitution
4x+5y+2 = 90
4x+5y = 90-2
4x+5y = 88
Now let's set up another equation and solve for x
B+C = 90
(x+4y+2)+(3y-3) = 90 ... substitution
x+7y-1 = 90
x = 90+1-7y
x = 91-7y
Go back to the first equation and plug in x = 91-7y. Solve for y.
4x+5y = 88
4(x)+5y = 88
4(91-7y)+5y = 88 ... replace x with 91-7y
364-28y+5y = 88
364-23y = 88
-23y = 88-364
-23y = -276
y = -276/(-23)
y = 12
Now that we know the value of y, we can use it to find x
x = 91-7y
x = 91-7(12) ... replace y with 12
x = 91-84
x = 7
So the x and y values are x = 7 and y = 12. We'll use both of these values to compute the measure of angle B
Angle B = (x+4y+2) degrees
Angle B = (7+4*12+2) degrees
Angle B = (7+48+2) degrees
Angle B = 57 degrees