To determine the sum of the measures of the angles in a 16-sided convex polygon, we can use the formula for the sum of the interior angles of an n-sided polygon. The formula is given by:
[tex]\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \][/tex]
where [tex]\( n \)[/tex] is the number of sides in the polygon.
For a 16-sided polygon:
1. Identify the number of sides ([tex]\( n \)[/tex]).
[tex]\[ n = 16 \][/tex]
2. Substitute [tex]\( n \)[/tex] into the formula:
[tex]\[ \text{Sum of interior angles} = (16 - 2) \times 180^\circ \][/tex]
3. Perform the subtraction inside the parentheses:
[tex]\[ (16 - 2) = 14 \][/tex]
4. Multiply the result by 180:
[tex]\[ 14 \times 180^\circ = 2520^\circ \][/tex]
Therefore, the sum of the measures of the angles in a 16-sided convex polygon is [tex]\( 2520^\circ \)[/tex].
The correct answer is:
b. 2520°
