Answer:
The measure of angle N is 68 degrees.
Step-by-step explanation:
Since this shape is a parallelogram, opposite angles will be equivalent. So to start, set (6x - 2) equal to (4x + 36).
— 6x - 2 = 4x + 36
Next, subtarct the 4x from both sides of the equation as well as add 2 to both sides of the equation an simplify.
— 6x - 4x - 2 + 2 = 4x - 4x + 36 + 2
— 2x = 38
Now, divide both sides of the equation by 2 to find the value of x.
— 2x/2 = 38/2
— x = 19
Finally, substitute 19 for every x in the original equation. Simplify.
— 6(19) - 2 = 4(19) + 36
— 114 - 2 = 76 + 36
— 112 = 112
We now know that these two angles are 112 degrees. If a parallelogram's angles must add up to 360 degrees, then subtract 112 twice from 360 to find the combined total angle measure of N and Q. Then divide that number by 2 to find the measure of N.
— 360 - 112 - 112 = 136
— 136/2 = 68
The measure of angle N is 68 degrees.
