The calculated measure of the angle N is 92 degrees
How to determine the measure of the angle N
From the question, we have the following parameters that can be used in our computation:
∠M = 3x + 1
∠N = 3x -8
∠O= x + 82
∠P = 2x + 15
The sum of angles in a quadrilateral is 360 degrees
So, we have
M + N + O + P = 360
Substitute the known values into the equation
3x + 1 + 3x - 8 + x + 82 + 2x - 15 = 360
Collect the like terms
3x + 3x + x + 2x = 360 - 1 + 8 - 82 + 15
9x = 300
Divide through by 9
x = 100/3
Recall that
∠N = 3x -8
So, we have
∠N = 3 * 100/3 - 8
∠N = 92
Hence, the measure of the angle N is 92 degrees
Question
The angles of a quadrilateral MNOP have measures:
∠M = 3x + 1
∠N = 3x -8
∠O= x+82
∠P = 2x + 15
Find the measure of ∠N.