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m < B = 55°

Step-by-step explanation:

The exterior angle of a triangle is the angle formed between one side of a triangle and the extension of its adjacent side. In this given problem, the exterior angle of the Δ ABC is < C. The remote interior angles of < C are < B and < A. The sum of these two remote interior angles is equal to the m < C.  

We're also given the information that m< C = 115°, m < A = 4y°, and m < B = (3y + 10)°

Therefore, to solve for the m < B, we can establish the following formula:

m < A + m < B = m < C

4y° + (3y + 10)° = 115°

4y° + 3y° + 10° = 115°

Add like terms:

7y° + 10° = 115°

Subtract 10° from both sides:

7y° + 10° - 10°  = 115° - 10°  

7y° = 105°

Divide both sides by 7 to solve for y:

7y°/7 = 105°/7

y = 15°

Therefore, the value of y = 15. To verify whether this is the correct value, substitute y = 15 into the equality statement:

m < A + m < B = m < C

4(15)° + [3(15) + 10]° = 115°

60° + 55° = 115°

115° = 115° (True statement, which means that y = 15 is the correct value).

Therefore, m < B = (3y + 10)° = 55°

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