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°
