Question

the blueprint shows the floor of a circus tent shaped like a regular 16 - sided polygon. at one corner of the tent, 4 sections of flooring come together to divide the corner into 4 equal angles. what is the measure of each of the 4 angles? explain.
the angle sum of a regular 16 - gon is \\(\square\\)°. the measure of each interior angle is \\(\square\\)°. the measure of each of the 4 equal angles that make up an interior angle is \\(\square\\)°. (type whole numbers or decimals)

Explanation:

Step1: Calculate interior angle sum

The formula for the sum of interior angles of an $n$-gon is $(n-2)\times180^\circ$. For $n=16$:
$$(16-2)\times180^\circ = 14\times180^\circ = 2520^\circ$$

Step2: Find each interior angle

Divide the total sum by the number of angles (16):
$$\frac{2520^\circ}{16} = 157.5^\circ$$

Step3: Split angle into 4 equal parts

Divide the interior angle by 4:
$$\frac{157.5^\circ}{4} = 39.375^\circ$$

Answer:

The angle sum of a regular 16-gon is $2520^\circ$. The measure of each interior angle is $157.5^\circ$. The measure of each of the 4 equal angles that make up an interior angle is $39.375^\circ$.