Define polygon, give examples, and solve geometry problems involving interior angles and number of sides.

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6. Define the term polygon. Give two examples of polygons.
A polygon is a closed two-dimensional shape made up of straight line segments connected end-to-end.
Examples: Triangle, Square.

7. Find the measure of each interior angle of a regular hexagon.

Identify the number of sides for a hexagon.
A hexagon has $n=6$ sides.
Use the formula for the measure of each interior angle of a regular polygon.
The formula is $\frac{(n-2) \times 180^\circ}{n}$ .
Substitute $n=6$ into the formula and calculate.
$\text{Interior Angle} = \frac{(6-2) \times 180^\circ}{6}$ $\text{Interior Angle} = \frac{4 \times 180^\circ}{6}$ $\text{Interior Angle} = \frac{720^\circ}{6}$ $\text{Interior Angle} = \boxed{\text{}120^\circ\text{}}$
8. A polygon has an interior angle sum of $1260^\circ$ . Calculate the number of sides it has.
Use the formula for the sum of interior angles of a polygon.
The formula is $(n-2) \times 180^\circ$ .
Set the formula equal to the given sum and solve for $n$ .
$(n-2) \times 180^\circ = 1260^\circ$ $n-2 = \frac{1260}{180}$ $n-2 = 7$ $n = 7 + 2$ $n = \boxed{\text{}9\text{}}$
9. One angle of a regular polygon measures $150^\circ$ . Find the number of sides.
Use the formula for one interior angle of a regular polygon.
The formula is $\frac{(n-2) \times 180^\circ}{n}$ .
Set the formula equal to the given angle and solve for $n$ .
$\frac{(n-2) \times 180^\circ}{n} = 150^\circ$ $(n-2) \times 180 = 150n$ $180n - 360 = 150n$ $180n - 150n = 360$ $30n = 360$ $n = \frac{360}{30}$ $n = \boxed{\text{}12\text{}}$
10. Draw a regular Octagon.
I cannot provide a visual drawing. However, a regular octagon is a polygon with 8 equal sides and 8 equal interior angles. Each interior angle of a regular octagon measures $135^\circ$ .

Define polygon, give examples, and solve geometry problems involving interior angles and number of sides.

Step-by-step solution

Identify the number of sides for a hexagon.

Use the formula for the measure of each interior angle of a regular polygon.

Substitute $n=6$ into the formula and calculate.

Use the formula for the sum of interior angles of a polygon.

Set the formula equal to the given sum and solve for $n$ .

Use the formula for one interior angle of a regular polygon.

Set the formula equal to the given angle and solve for $n$ .

Still stuck on this one?

More Mathematics Questions

Define polygon, give examples, and solve geometry problems involving interior angles and number of sides.

Step-by-step solution

Identify the number of sides for a hexagon.

Use the formula for the measure of each interior angle of a regular polygon.

Substitute n=6n=6n=6 into the formula and calculate.

Use the formula for the sum of interior angles of a polygon.

Set the formula equal to the given sum and solve for nnn.

Use the formula for one interior angle of a regular polygon.

Set the formula equal to the given angle and solve for nnn.

Still stuck on this one?

More Mathematics Questions

Substitute $n=6$ into the formula and calculate.

Set the formula equal to the given sum and solve for $n$ .

Set the formula equal to the given angle and solve for $n$ .