m < 105° and m < (10x + 15)° have the same measure because they are alternate interior angles that do not have a common vertex on alternate sides of the transversal. Since they have the same measure, we can solve for x:
m < 105° = m < 10x° + 15 °
Subtract 15 from both sides:
m < 105° - 15° = 10x°
90° = 10x°
Divide both sides by 10 to solve for x:
90°/10 = 10x/10
9° = x
Therefore, the value of x = 9°
Substitute this value into m < (10x + 15)° to find its true measure:
10(9) + 15 = 90 + 15 = 105°
This proves my statements earlier that m < 105° has the same measure as m < (10x + 15)°
The correct answer is x = 9°
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