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If m ∥ n, m∠1 = 4x − 6, and m∠7 = 2x + 40, then what is m∠1?

A. 10 degrees
B. 20 degrees
C. 30 degrees
D. 40 degrees

1 Answer

5 votes

Final answer:

To find the measure of angle m∠1, we need to use the given information that m and n are parallel lines and m∠1 = 4x - 6. By setting up and solving an equation, we find that the measure of angle m∠1 is 86 degrees.

Step-by-step explanation:

To find the measure of angle m∠1, we need to use the given information that m and n are parallel lines and m∠1 = 4x - 6. Since m and n are parallel lines, the corresponding angles formed by the transversal line n are congruent. Therefore, m∠1 is equal to m∠7 which is given as 2x + 40. So we can set up an equation:

4x - 6 = 2x + 40

Now, let's solve for x:

4x - 2x = 40 + 6

2x = 46

x = 23

Now substitute the value of x in m∠1 = 4x - 6:

m∠1 = 4(23) - 6

m∠1 = 92 - 6

m∠1 = 86

Therefore, the measure of angle m∠1 is 86 degrees. So, the correct answer is D. 40 degrees.

User Anton Gogolev
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