Given that m < 1 = 5x, and m <2 = 9x, and that they are complementary angles with a sum of 90°:
We can establish the following formula:
m < 1 + m < 2 = 90°
Substitute the given values into the formula:
5x + 9x = 90°
Add like terms:
14x = 90°
Divide both sides by 14:
14x / 14 = 90° / 14
x = 6.42857
Substitute the value of x into m < 1:
m < 1 = 5x = 5(6.42857)
m < 1 = 32.1°
To verify whether we have the correct value for x, let’s substitute its value into the original equation:
m < 1 + m < 2 = 90°
5x + 9x = 90°
32.1 + 9(6.42857) = 90°
32.1 + 57.9 = 90°
90° = 90° (True statement. Therefore, we derived the correct value for x).
Therefore, the correct answer is: m < 1 = 32.1°
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