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Difficulty:
25%
(medium)
Question Stats:
76% (01:33) correct
23% (01:00) wrong based on 21 sessions
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A regular polygon is defined as a polygon with all sides congruent and all angles congruent. In a regular polygon with n sides, the measure of one interior angle is equal to 168°. What is the value of n?
A. 12
B. 18
C. 24
D. 30
E. 36
A. 12
B. 18
C. 24
D. 30
E. 36
02 Nov 2025, 10:26
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Official Explanation
The sum of the measures of the interior angles on an n-sided polygon is given by the formula Angle Sum = \(180(n – 2)\) degrees. A polygon with n sides also has n angles, and if each angle measures 168°, then the sum of all angles equals 168n. So we can set \(180(n – 2) = 168n.\) Distribute 180, and \(180n – 360 = 168n.\) Subtract 168n and add 360 to each side to obtain \(12n = 360.\) Divide by 12, and n = 30, (D).
Answer: D
The sum of the measures of the interior angles on an n-sided polygon is given by the formula Angle Sum = \(180(n – 2)\) degrees. A polygon with n sides also has n angles, and if each angle measures 168°, then the sum of all angles equals 168n. So we can set \(180(n – 2) = 168n.\) Distribute 180, and \(180n – 360 = 168n.\) Subtract 168n and add 360 to each side to obtain \(12n = 360.\) Divide by 12, and n = 30, (D).
Answer: D
