Answer:
The regular polygon has 72 sides ⇒ A
Step-by-step explanation:
The rule of the measure of an interior angle of a regular polygon is:
The measure of each angle = [tex]\frac{(n-2)180}{n}[/tex] , where n is the number of its sides
Let us use this rule to solve the question
∵ The polygon is regular
∴ All sides are equal in lengths
∴ All interior angles are equal in measures
∵ The measure of an interior angle of the regular polygon is 175°
→ Substitute it in the rule above to find n
∴ 175° = [tex]\frac{(n-2)180}{n}[/tex]
→ Multiply both sides by n to cancel the denominator in the right side
∴ 175 n = (n - 2)180
→ Multiply the bracket by 180
∴ 175 n = n(180) - 2(180)
∴ 175 n = 180 n - 360
→ Subtract 180 n from both sides
∵ 175 n - 180 n = 180 n - 180 n - 360
∴ - 5 n = - 360
→ Divide both sides by -5
∵ [tex]\frac{-5n}{-5}=\frac{-360}{-5}[/tex]
∴ n = 72
∴ The regular polygon has 72 sides
