If the sum of the measures of interior angles of a regular convex polygon is 1620° how many sides does a polygon have find the m
easure of one interior angle and one exterior angle
2 answers:
Answer:
- the polygon has 11 sides
- one interior angle measures 147 3/11 degrees
- one exterior angle measures 32 8/11 degrees
Step-by-step explanation:
The relation between the number of sides (n) and the total degree measure of interior angles is ...
angle total = 180° × (n -2)
We can find n by filling in the given total and solving:
1620 = 180(n -2)
1620/180 = 9 = n -2
9 + 2 = 11 = n
The number of sides is 11.
The measure of one interior angle is 1620°/11 = 147 3/11 degrees.
The measure of one exterior angle is 360°/11 = 32 8/11 degrees.
Answer:
Step-by-step explanation:
(n-2)180=1620
n-2=1620/180=9
n=9+2=11
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