The Polygon Angle-Sum Theorem

Front

What is the Polygon Angle-Sum Theorem?

Back

The Polygon Angle-Sum Theorem states that the sum of the interior angles of a polygon with n sides is given by the formula: \( (n - 2) \times 180^\circ \).

Front

How do you find the sum of the interior angles of a hexagon?

Back

For a hexagon (6 sides), use the formula: \( (6 - 2) \times 180^\circ = 720^\circ \).

Front

What is the measure of one interior angle of a regular polygon with 8 sides?

Back

For a regular octagon, the measure of one interior angle is: \( \frac{(8 - 2) \times 180^\circ}{8} = 135^\circ \).

Front

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

Back

The measure of one exterior angle of a regular polygon is given by: \( \frac{360^\circ}{n} \), where n is the number of sides.

Front

What is the measure of one exterior angle of a regular decagon?

Back

For a regular decagon (10 sides), the measure of one exterior angle is: \( \frac{360^\circ}{10} = 36^\circ \).

Front

If the interior angle sum of a polygon is 1800°, how many sides does it have?

Back

Using the formula: \( n = \frac{1800 + 360}{180} = 12 \), the polygon has 12 sides.

Front

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

Back

The interior and exterior angles of a polygon are supplementary, meaning they add up to 180°.

Front

How do you find the missing angle in a polygon?

Back

To find a missing angle, subtract the sum of the known angles from the total interior angle sum: \( (n - 2) \times 180^\circ \).

Front

What is the sum of the interior angles of a triangle?

Back

The sum of the interior angles of a triangle is always 180°.

Front

What is the sum of the interior angles of a quadrilateral?

Back

The sum of the interior angles of a quadrilateral is always 360°.