Question 515114
The sum of the measures of the three interior angles of a triangle on the plane is always 180 degrees.  You are given the measures of all three angles as expressions involving x.  Let's set up an algebraic equation and solve for x:

measure(A) + measure(B) + measure(C) = 180
{{{(3x + 27) + (5x - 13) + (4x + 24) = 180}}}
{{{ 12x + 38 = 180 }}} (combining like terms)
{{{ 12x = 142 }}} (subtracting 38 from both sides)
{{{ x = 142/12 }}} (dividing both sides by 12)
{{{ x = 71/6 }}} (reducing the fraction on the right side)

So {{{x = 71/6}}}, but the question asks for the measure of angle B, so we substitute {{{71/6}}} in for the expression for the measure of B:

{{{5x - 13 = 5*(71/6) - 13 = 355/6 - 13 = 355/6 - 78/6 = 277/6}}} degrees

So the measure of angle B is {{{277/6}}}, or 46 1/6 degrees.  Now this is not a very nice number, so let's check that we didn't make a mistake by finding the measures of angles A and C and then seeing if the measures of all three angles sum to 180 degrees.

measure(A) = {{{3x + 27 = 3*(71/6) + 27 = 213/6 + 27 = 213/6 + 162/6 = 375/6 }}} degrees

measure(C) = {{{4x + 24 = 4*(71/6) + 24 = 284/6 + 24 = 284/6 + 144/6 = 428/6 }}} degrees

measure(A) + measure(B) + measure(C) = 375/6 + 277/6 + 428/6 = 1080/6 = 180}}} degrees

So we were correct: the measure of angle B is {{{277/6}}}, or 46 1/6 degrees.