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!)

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

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