Answer:
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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