Day 74

Front

What is the formula to find the measure of each exterior angle of a regular polygon?

Back

The measure of each exterior angle of a regular polygon can be found using the formula: \( \text{Exterior Angle} = \frac{360}{n} \), where \( n \) is the number of sides.

Front

How do you calculate 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: \( \text{Sum} = (n - 2) \times 180 \), where \( n \) is the number of sides.

Front

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

Back

The measure of one interior angle in a regular polygon can be calculated using the formula: \( \text{Interior Angle} = \frac{(n - 2) \times 180}{n} \).

Front

If the exterior angle of a polygon is 15 degrees, how many sides does it have?

Back

To find the number of sides, use the formula: \( n = \frac{360}{\text{Exterior Angle}} \). For 15 degrees, \( n = \frac{360}{15} = 24 \).

Front

What is the measure of each exterior angle of a regular 67-gon?

Back

The measure of each exterior angle of a regular 67-gon is \( \frac{360}{67} \approx 5.4 \) degrees.

Front

What is the angle sum of the interior angles of a polygon with 10 sides?

Back

Using the formula \( (n - 2) \times 180 \), for a 10-sided polygon, the sum is \( (10 - 2) \times 180 = 1440 \) degrees.

Front

What is the measure of one interior angle in a regular pentagon?

Back

For a regular pentagon (5 sides), the measure of one interior angle is \( \frac{(5 - 2) \times 180}{5} = 108 \) degrees.

Front

How many sides does a polygon have if the sum of its interior angles is 1260 degrees?

Back

Using the formula \( (n - 2) \times 180 = 1260 \), we can solve for \( n \): \( n = \frac{1260}{180} + 2 = 10 \).

Front

What is the relationship between the number of sides and the exterior angle of a regular polygon?

Back

The exterior angle decreases as the number of sides increases; specifically, as the number of sides increases, each exterior angle approaches 0 degrees.

Front

If a regular polygon has 12 sides, what is the measure of each interior angle?

Back

For a 12-sided polygon, the measure of each interior angle is \( \frac{(12 - 2) \times 180}{12} = 150 \) degrees.