Answer:
n = 8
Step-by-step explanation:
Two angles are vertical angles if they are opposite angles formed by the intersection of two lines. Vertical angles are congruent.
Given that m < (9n)° and m < (8n + 8)° are vertical angles, then it means that they have the same measure. Therefore, we can solve for the value of n by establishing the following equation:
9n = (8n + 8)
9n = 8n + 8
Subtract 8n from both sides:
9n - 8n = 8n - 8n + 8
n = 8
To double-check whether we came up with the correct value for n, substitute n = 8 into the equation:
9n = (8n + 8)
9(8) = [8(8) + 8]
72 = 64 + 8
72 = 72 (True statement)
Therefore, the correct answer is n = 8.
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