A Nonagon Has Angles That Measure 153.7°, 123°, 126°, 166.6°, 138°, 113°, 141°, 136….

A nonagon has angles that measure 153.7°, 123°, 126°, 166.6°, 138°, 113°, 141°, 136.6°, and n. What is n?

Answer:

n = 162.1°

Step-by-step explanation:

Use this formula to find the total measure of interior angles of a polygon:

(n-2) × 180°  where n is the number of sides.

A nonagon is a polygon with 9 sides.

To find the total measure of a nonagon’s interior angles where n=9:

(9 – 2) × 180°

= 7 × 180°

= 1,260°  ⇒  total measure of a nonagon’s interior angles

To solve for the missing measure of the 9th angle, n:

n = 1,260° – (153.7° + 123° + 126° + 166.6° + 138° + 113° + 141° + 136.6°)

n = 1,260° – 1097.9°

n = -162.1°

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