Each side of a regular convex polygon subtends an angle of 30° at its center. Calculate each interior angle
Question 1 Report
Each side of a regular convex polygon subtends an angle of 30° at its center. Calculate each interior angle
Answer Details
A regular convex polygon has equal angles and equal sides. Therefore, to calculate the interior angle of a regular convex polygon, we can use the formula:
Interior angle = (n - 2) x 180 / n
where n is the number of sides of the polygon.
In this case, we know that each side subtends an angle of 30° at the center, which means that there are 12 sides in the polygon (since 360° / 30° = 12). Substituting this value into the formula, we get:
Interior angle = (12 - 2) x 180 / 12
= 10 x 180 / 12
= 150°
Therefore, each interior angle of the regular convex polygon is 150°. The answer is.
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