Question

A pair of parallel lines is cut by a transversal. A pair of parallel lines is shown cut by a transversal. Angle A is located in the upper left exterior next to the transversal, and angle B is located in the bottom right exterior corner of the transversal. If M∠A = (6x − 3)° and M∠B = (9x − 24)°, what is the value of x?

a. 1.4
b. 7
c. 7.8
d. 13.8

Answer 1

To solve for x, the equation 6x - 3 = 9x - 24 is formed by setting the measures of the corresponding angles equal to each other. After simplifying, the value of x is found to be 7.

Step-by-step explanation:

When a pair of parallel lines is cut by a transversal, corresponding angles are congruent.

The two intersections generated by a transversal cutting through two parallel lines form many angles. Transversal angles are what those are known as. Following are examples of those kinds of angles on a transversal:

Matching angles

Different interior angles

Various Exterior Angles

Co-interior Angles

Thus, if M∠A = (6x - 3)° and M∠B = (9x - 24)°, and angles A and B are corresponding angles, then we can set their measures equal to each other to solve for x.

The equation will be 6x - 3 = 9x - 24. Solving for x, we subtract 6x from both sides to get -3 = 3x - 24. Then, add 24 to both sides to obtain 21 = 3x, and finally, we divide both sides by 3 to find x = 7.