Question

Find the value of the variable if m is parallel to l, and the measure of ∠1 is 2x + 44, and the measure of ∠5 is 5x + 38.

a) x = 6
b) x = 8
c) x = 11
d) x = 13

Answer 1

By using the property of corresponding angles being congruent when lines are parallel, the value of x = 2, which does not match any of the provided options.

Step-by-step explanation:

To find the value of the variable x when lines m is parallel to line l, and given that the measure of ∠1 is 2x + 44, and the measure of ∠5 is 5x + 38, we use the concept that corresponding angles formed by a transversal with two parallel lines are congruent. This means that ∠1 and ∠5 are equal in measure.

Setting the measures equal to each other gives us the equation 2x + 44 = 5x + 38. Simplifying this equation by subtracting 2x from both sides yields 44 = 3x + 38. Further simplification by subtracting 38 from both sides gives 6 = 3x, and dividing both sides by 3 yields x = 2.

Therefore, the correct value of x is 2, which is not listed in the options a), b), c), or d).