Answer: 59 degrees
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Work Shown:
We have the three angles:
angle A = (3x+2) degrees
angle B = (2x+7) degrees
angle C = 41 degrees
Rule: for any triangle, the three angles add up to 180 degrees
(angle A) + (angle B) + (angle C) = 180
(3x+2) + (2x+7) + (41) = 180
3x+2 + 2x+7 + 41 = 180
(3x+2x)+(2+7+41) = 180
(5x)+(50) = 180
5x+50 = 180
5x+50-50 = 180-50
5x = 130
5x/5 = 130/5
x = 26
Now use this x value to find the measure of angle B
angle B = (2x+7) degrees
angle B = (2*x+7) degrees
angle B = (2*26+7) degrees
angle B = (52+7) degrees
angle B = 59 degrees
Side Note: Angle A is 80 degrees (3x+2 = 3*26+2 = 78+2 = 80)
Another thing to note: A+B+C = 80+59+41 = 180
