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QuestionFind the formula for one interior angle of a polygon with nn sides. Use the formula (n−2)⋅180n\frac{(n-2) \cdot 180}{n}.

Studdy Solution

STEP 1

Assumptions1. We are dealing with a simple polygon (not self-intersecting). . The polygon is convex (all interior angles are less than180 degrees).
3. The number of sides of the polygon is known.

STEP 2

The sum of the interior angles of a polygon can be found using the formulaSum of interior angles=(n−2)×180∘Sum\, of\, interior\, angles = (n -2) \times180^\circwhere nn is the number of sides of the polygon.

STEP 3

To find one interior angle of a regular polygon (where all sides and angles are equal), we can divide the sum of the interior angles by the number of sides.
One interior angle=(n−2)×180∘nOne\, interior\, angle = \frac{(n -2) \times180^\circ}{n}This is the rule to find one interior angle of a polygon.

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