Question

Line l || m and line n ||o. If the m∠12 = 4x + 14 and the m∠9 = 7x + 23, then what is the m∠9?

Answer 1

To find the measure of angle 9, we can set up the equation 4x + 14 = 7x + 23, where x represents the angle measure. Solving this equation yields x = -3, and plugging it back into the equation gives the measure of angle 9 as 2 degrees.

Step-by-step explanation:

To find the measure of angle 9, we need to set up an equation using the given information. We know that line m is parallel to line l and line n is parallel to line o. When two parallel lines are intersected by a transversal, corresponding angles are congruent. This means that angle 12 is congruent to angle 9. So we can set up the equation:

4x + 14 = 7x + 23

Next, we can solve this equation to find the value of x. Subtracting 4x from both sides gives:

14 = 3x + 23

Then, subtracting 23 from both sides gives:

-9 = 3x

Dividing both sides by 3 gives:

x = -3

Now that we know the value of x, we can substitute it back into the equation to find the measure of angle 9. Plugging in x = -3 gives:

7(-3) + 23 = -21 + 23 = 2

Therefore, the measure of angle 9 is 2 degrees.