Question

Find the value of the variable if m || n, m₂ = (3x + 15), and m₇ = (4x + 5). What is m₇?

A. m₇ = 12x
B. m₇ = 18x
C. m₇ = 20x
D. m₇ = 21x
E. m₇ = 4x

Answer 1

By setting the expressions for corresponding angles m₂ and m₇ equal to each other and solving for x, we find that the measure of angle m₇ is 45 degrees.

Step-by-step explanation:

If lines m and n are parallel (notated as m || n), then corresponding angles created by a transversal intersecting these lines are congruent. In this case, angle m₂ and angle m₇ are corresponding angles. Therefore, we can set the expressions for these angles equal to each other because their measures will be the same.

Here is the step-by-step solution:

1. Set the expressions equal to each other: 3x + 15 = 4x + 5.
2. Solve for x: Subtract 3x from both sides to get 15 = x + 5.
3. Then subtract 5 from both sides to get x = 10.
4. Now, substitute x with 10 in either m₂ or m₇ to find the measure of the angles. Using m₇ we get m₇ = 4(10) + 5 = 45.

Therefore, the measure of angle m₇ is 45 degrees.