Question

If angle A and angle B are alternate exterior angles and angle A = (4x + 1)degrees and angle

B = (7x - 14)degrees, what is the measure of angle A?

Answer 1

To find the measure of angle A, we set the alternate exterior angles equal, solve for x, and then substitute back into the expression for angle A, which results in angle A being 21 degrees.

Step-by-step explanation:

If angle A and angle B are alternate exterior angles and angle A is given by (4x + 1) degrees and angle B by (7x - 14) degrees, to find the measure of angle A, we use the property that alternate exterior angles are equal when the lines are parallel. Therefore, we set up the equation 4x + 1 = 7x - 14 and solve for x.

1. First, subtract 4x from both sides: 1 = 3x - 14.
2. Next, add 14 to both sides: 15 = 3x.
3. Finally, divide both sides by 3: x = 5.
4. Now that we have the value for x, we substitute it back into the expression for angle A: angle A = 4(5) + 1 = 20 + 1 = 21 degrees.

Therefore, the measure of angle A is 21 degrees.