m∠B = 56.2
Step-by-step explanation:
in ΔABC:
m ∠A = 75
m∠B = 2x + 5
m∠C = 3x - 28
The sum of angles in triangle ABC:
m∠A + m∠B + m∠C = 180° (sum of angles in a triangle)
75 + 2x + 5 + 3x - 28 = 180
collect like terms:
75 + 5 - 28 + 2x + 3x = 180
52 + 5x = 180
subtract 52 from both sides:
5x = 180 - 52
5x = 128
Divide both sides by 5:
x = 128/5
x = 25.6
To get m∠B, we will substitute for x:
m∠B = 2(25.6) + 5
m∠B = 56.2