Find the measure of angle n. 150° 8° 90° 294°

The correct answer is: The measure of angle N, m∠N, is 150° (Option A)

Explanation:

Since the geometric figure in the picture is polygon having five sides (n=5), the sum of interior angles will be the following:

Sum of interior angles = (n-2) * 180°

Sum of interior angles = (5-2) * 180° = 540°

The (individual) interior angles are as follows:

∠P = 90°

∠O = 90°

∠L = (17x+4)°

∠N = (18x+6)°

∠M = (10x-10)°

Now add all the interior angles and equate them with 540°, as follows:

∠P + ∠O + ∠L + ∠N + ∠M = 540°

90° + 90° + (17x + 4)° + (18x+6)° + (10x-10)° = 540°

45x° + 180° = 540°

45x° = 360°

x = 8°

Now that we have the values of x, it's time to find the value of N by plugging in the value of x in the following expression:

∠N = (18x+6)° --- (A)

Plug in the value of x in (A):

∠N = (18*8 + 6)°

∠N = 150°

Hence, the measure of angle N, m∠N, is 150° (Option A)

NOTE: Please do not confuse ∠N with the value of x. The x is 8, whereas the m∠N is 150°. (as 8° is also present in the options; so be very careful!)