To solve the given problem, let's analyze the interior angles of a regular 20-sided polygon.
1. Formula for the Interior Angle of a Regular Polygon:
The formula to determine the measure of an interior angle of a regular [tex]\( n \)[/tex]-sided polygon is:
[tex]\[
\text{Interior angle} = \frac{(n-2) \times 180^\circ}{n}
\][/tex]
Where [tex]\( n \)[/tex] is the number of sides of the polygon.
2. Substitute [tex]\( n = 20 \)[/tex]:
For a 20-sided polygon ([tex]\( n = 20 \)[/tex]):
[tex]\[
\text{Interior angle} = \frac{(20-2) \times 180^\circ}{20}
\][/tex]
3. Calculate the Interior Angle:
[tex]\[
\text{Interior angle} = \frac{18 \times 180^\circ}{20}
\][/tex]
[tex]\[
\text{Interior angle} = \frac{3240^\circ}{20}
\][/tex]
[tex]\[
\text{Interior angle} = 162^\circ
\][/tex]
4. Match the Interior Angle with the Given Choices:
Among the given choices for [tex]\( g \)[/tex]:
[tex]\[
g = 180^\circ, \quad g = 162^\circ, \quad g = 60^\circ, \quad g = 54^\circ
\][/tex]
The calculated interior angle of the 20-sided polygon is [tex]\( 162^\circ \)[/tex]. Therefore, the value that matches the interior angle of the polygon from the given choices is:
[tex]\[
g = 162
\][/tex]
Thus, the value of [tex]\( g \)[/tex] is [tex]\( \boxed{162} \)[/tex].
