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 ______

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

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.
----------------
A + B + C = 180 degrees
3x+27 + 5x-13 + 4x+24 = 180
12x + 38 = 180
12x = 142
x = 11 5/6
----
B = 5x-13 = 5(11 5/6) -13 = 46.1667 degrees
=======================================
Cheers,
Stan H.
============

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.
RELATED QUESTIONS
Suppose parallelogram has angles defined by the following expressions: angle A = 6x + 19; (answered by KMST)
the angles of a triangle have the following measures: angle A= (3x+8) degrees; angle B =... (answered by edjones)
Angle A and Angle B are supplementary angles. If mAngleA = (2x-24) and mAngleB = (5x-27), (answered by Boreal)
Find the unknown angle for the following right triangle: Angle A Angle B... (answered by Alan3354)
if two angles in the ratio of 5:4 are represented by 5x and 4x express each of the... (answered by dkppathak)
Please help me solve this equation. the variable expressions represent the angle... (answered by rfer,stanbon)
In triangle ABC, measure angle A=5x, measure angle B =4x+30,and measure angle C= 80-2x.... (answered by ilana)
Angles A and B are complementary. Find the measures of each angle. Angle A = 3/4x - 13 (answered by Leaf W.)
Prove the following theorem: The acute angles of a right triangle are complementary.... (answered by richard1234)