To determine the sum of the measures of the interior angles of a decagon, we use the formula that applies to any convex polygon:
[tex]\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \][/tex]
where:
- [tex]\( n \)[/tex] is the number of sides of the polygon.
A decagon has 10 sides.
1. Substitute [tex]\( n = 10 \)[/tex] into the formula:
[tex]\[ \text{Sum of interior angles} = (10 - 2) \times 180^\circ \][/tex]
2. Simplify the expression:
[tex]\[ \text{Sum of interior angles} = 8 \times 180^\circ \][/tex]
3. Calculate the product:
[tex]\[ \text{Sum of interior angles} = 1440^\circ \][/tex]
Therefore, the sum of the measures of the interior angles of a decagon is [tex]\( 1440^\circ \)[/tex].
The correct answer is:
A. [tex]\( 1440^\circ \)[/tex]
