Interior and Exterior Angles of Polygons

Front

What is an exterior angle of a polygon?

Back

An exterior angle is formed by one side of a polygon and the extension of an adjacent side. The sum of the exterior angles of any polygon is always 360°.

Front

How do you calculate the measure of each exterior angle of a regular polygon?

Back

To find the measure of each exterior angle of a regular polygon, use the formula: Exterior Angle = 360° / n, where n is the number of sides.

Front

If an exterior angle of a regular polygon measures 15°, how many sides does it have?

Back

24 sides (calculated using the formula: n = 360° / 15°).

Front

What is the formula to find the sum of the interior angles of a polygon?

Back

The sum of the interior angles of a polygon can be calculated using the formula: (n - 2) × 180°, where n is the number of sides.

Front

What is the measure of EACH exterior angle of a 21-gon?

Back

17.14° (calculated using the formula: 360° / 21).

Front

If the measures of a heptagon are 127°, 152°, 112°, 123°, 135°, and 105°, what is the measure of the remaining angle?

Back

146° (calculated by first finding the sum of the interior angles of a heptagon, which is 900°, and then subtracting the sum of the given angles).

Front

What is the measure of each interior angle of a regular hexagon?

Back

120° (calculated using the formula: (6 - 2) × 180° / 6).

Front

What is the relationship between interior and exterior angles of a polygon?

Back

The interior angle and exterior angle at each vertex of a polygon are supplementary, meaning they add up to 180°.

Front

How many sides does a polygon have if each exterior angle measures 30°?

Back

12 sides (calculated using the formula: n = 360° / 30°).

Front

What is the measure of each interior angle of a regular octagon?

Back

135° (calculated using the formula: (8 - 2) × 180° / 8).