Final answer:
To find the measure of angle L in the parallelogram LMNO with given angles, set up an equation and solve for x. Substitute the value of x into angle L to find its measure.
Step-by-step explanation:
To find the measure of angle L in the parallelogram LMNO, we need to know the value of angle L.
Given that angle L is equal to 9x + 92 and angle M is equal to 3x + 40, we can set up an equation:
9x + 92 = 180 - (3x + 40)
Simplifying the equation, we get:
9x + 92 = 180 - 3x - 40
Combining like terms, we have:
12x + 92 = 140 - 3x
Adding 3x to both sides, we get:
15x + 92 = 140
Subtracting 92 from both sides, we get:
15x = 48
Dividing both sides by 15, we get:
x = 48 / 15 = 3.2
Now we can substitute the value of x into angle L:
angle L = 9(3.2) + 92
= 28.8 + 92
= 120.8 degrees