413,607 views
10 votes
10 votes
44. Given ΔABC, with m

User Darrylyeo
by
3.0k points

1 Answer

14 votes
14 votes

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

User Ben Mosher
by
2.4k points