To determine the measure of the interior angles in a regular heptagon, we can use the formula
n(n−2)×180∘where n represents the number of sides of the polygon.
A heptagon is defined as a seven-sided polygon. In the case of a regular heptagon, all sides and angles are congruent. To find the measure of each interior angle, we first need to calculate the sum of all the interior angles of the heptagon. The formula for the sum of the interior angles of any polygon is
(n−2)×180∘where n is the number of sides. For a heptagon, we have n=7.
By substituting 7 into the formula, we can compute the sum of the interior angles:
(7−2)×180∘=5×180∘=900∘This indicates that the total sum of all the interior angles in a heptagon is 900∘.
Since a regular heptagon has equal interior angles, we can find the measure of each angle by dividing the total sum by the number of angles (which is the same as the number of sides, 7):
7900∘≈128.57∘Consequently, each interior angle in a regular heptagon measures approximately 128.57∘. This approach can be applied to any regular polygon by substituting the correct number of sides into the formulas provided.
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| All of our elite tutors are full-time professionals, with at least five years of tuition experience and over 5000 accrued teaching hours in their subject. |
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International Tuition |
| Based in Cambridge, with operations spanning the globe, we can provide our services to support your family anywhere. |
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Independent School Entrance Success |
| Our families consistently gain offers from at least one of their target schools, including Eton, Harrow, Wellington and Wycombe Abbey. |
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