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A craft designer is creating a symmetrical pattern using a sequence of angles in a polygonal tile. The tile has five sides, and the interior angles are to be determined using a debugging algorithm.
The algorithm calculates the sum of interior angles using the formula (n - 2) × 180°, where n is the number of sides. The algorithm then divides this sum by 5 to find the average interior angle.
However, the designer notices that one angle in the tile is 54°, and the algorithm incorrectly assumes all angles are equal. The designer tests the algorithm by inputting n = 5 and checks if the average angle matches the known value of 54°.
What is the exact value of the average interior angle for a regular pentagon, as calculated by the algorithm?
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Explanation
Worked solution and answer (click to reveal)
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Worked solution
- The polygon has 5 sides, so n = 5.
- The formula for the sum of interior angles of a polygon is (n - 2) × 180°.
- Substitute n = 5 into the formula: (5 - 2) × 180°.
- Calculate (5 - 2) = 3.
- Multiply 3 × 180° = 540°.
- The algorithm divides the sum by 5 to find the average interior angle.
- Substitute the sum: 540° ÷ 5.
- Perform the division: 540 ÷ 5 = 108.
- The average interior angle is 108°.
- The algorithm incorrectly assumes all angles are equal, but the correct average for a regular pentagon is 108°.
- The known value of 54° is not the average; it is one angle, which is not consistent with a regular pentagon.
- Therefore, the exact value of the average interior angle for a regular pentagon, as calculated by the algorithm, is 108°.
Reference answer: 108°
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