If two angles are alternate exteriors and one of them has the measure of 3x squared, and the other had a measure of 21x what are degree numbers
what is the math word for a line that divides a segment into smaller segments of equal length
bisector
To find the degree measures of the alternate exterior angles, we need to set up an equation using the given information.
Let's say the measure of one angle is 3x² (given) and the measure of the other angle is 21x (given). Since alternate exterior angles are congruent when a transversal intersects two parallel lines, we can set up the following equation:
3x² = 21x
To solve this equation, we first need to simplify it. Let's divide both sides of the equation by 3x:
3x² / 3x = 21x / 3x
This simplifies to:
x = 7
Now that we have the value of x, we can substitute it back into either of the angle measures to find the degree numbers. Let's substitute it into the measure of the first angle, which is 3x²:
Angle 1 = 3x² = 3(7)² = 3(49) = 147 degrees
Similarly, we can find the measure of the other angle:
Angle 2 = 21x = 21(7) = 147 degrees
Therefore, both alternate exterior angles have a measure of 147 degrees.