To find the measure of one interior angle of a regular 21-gon, we use the formula:
[tex]\[ \text{Interior Angle} = \frac{(n - 2) \times 180^\circ}{n} \][/tex]
Where [tex]\( n \)[/tex] is the number of sides of the polygon.
Step-by-step Solution:
1. Identify the number of sides [tex]\( n \)[/tex] of the polygon. In this case, [tex]\( n = 21 \)[/tex].
2. Substitute [tex]\( n = 21 \)[/tex] into the formula:
[tex]\[ \text{Interior Angle} = \frac{(21 - 2) \times 180^\circ}{21} \][/tex]
3. Calculate the value within the parentheses:
[tex]\[ 21 - 2 = 19 \][/tex]
4. Multiply this result by 180 degrees:
[tex]\[ 19 \times 180^\circ = 3420^\circ \][/tex]
5. Finally, divide by the number of sides (21):
[tex]\[ \frac{3420^\circ}{21} = 162.85714285714286^\circ \][/tex]
Thus, the measure of one interior angle of a regular 21-gon is approximately [tex]\( 162.857^\circ \)[/tex].
Comparing this to the given choices:
A. 165.6
B. 165
C. 162.9
D. 160
The answer closest to [tex]\( 162.857^\circ \)[/tex] is:
C. 162.9
