SOLUTION: Suppose a triangle has angles defined by the following expressions: angle A = 3x + 27; angle B = 5x - 13; and angle C = 4x + 24. Then the measure of angle B is ______

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Question 515114: Suppose a triangle has angles defined by the following expressions: angle A = 3x + 27; angle B = 5x - 13; and angle C = 4x + 24. Then the measure of angle B is _______ degrees
Found 2 solutions by stanbon, drcole:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Suppose a triangle has angles defined by the following expressions: angle A = 3x + 27; angle B = 5x - 13; and angle C = 4x + 24.
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A + B + C = 180 degrees
3x+27 + 5x-13 + 4x+24 = 180
12x + 38 = 180
12x = 142
x = 11 5/6
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B = 5x-13 = 5(11 5/6) -13 = 46.1667 degrees
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Cheers,
Stan H.
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Then the measure of angle B is _______ degrees

Answer by drcole(72) (Show Source):
You can put this solution on YOUR website!
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

(combining like terms)
(subtracting 38 from both sides)
(dividing both sides by 12)
(reducing the fraction on the right side)
So , but the question asks for the measure of angle B, so we substitute in for the expression for the measure of B:
degrees
So the measure of angle B is , 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) = degrees
measure(C) = 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 , or 46 1/6 degrees.

SOLUTION: Suppose a triangle has angles defined by the following expressions: angle A = 3x + 27; angle B = 5x - 13; and angle C = 4x + 24. Then the measure of angle B is _______ degrees