How do you use the properties of polygons & parallelograms to find missing sides & angles?

Question

How do you use the properties of polygons & parallelograms to find missing sides & angles?

Answer 1

POLYGONS:

You can find the sum of any polygon's interior angles by using the formula (n-2)*180, where n is the number of sides. For example, to find the sum of the interior angles of a pentagon with 5 sides (n=5), the sum of its interior angles is:

(n-2)*180 = (5-2)*180 = 3*180 = 540 degrees

The sum of any polygon's exterior angles is always 360 degrees.

For example, the sum of a pentagon's exterior angles is 360 degrees.

REGULAR POLYGONS:

Since a regular polygon has all sides and angles congruent, the measure of one interior angle is the sum of the interior angles divided by the number of sides: ((n-2)*180)/n

For example, the measure of one interior angle of a regular pentagon (n=5) is:

((n-2)*180)/n = ((5-2)*180)/5 = 540/5 = 108 degrees

To find the measure of one exterior angle in a regular polygon, divide the sum of the exterior angles (360 degrees) by the number of sides, n. For example, the measure of one exterior angle of a regular pentagon (n=5) is: 360/5 = 72 degrees

PARALLELOGRAMS:

The following properties of parallelograms can help you find missing sides/angles:

1. Opposite sides are both congruent (same length) and parallel (remember angle relationships for parallel lines cut by a transversal when you have a diagonal drawn in)
2. Opposite angles are congruent (same measure)
3. Consecutive/adjacent angles are supplementary (add up to 180 degrees)
4. Diagonals bisect each other

A diagram with markings illustrating the properties here: https://mathmonks.com/parallelogram

*Note: Be careful when you are working with special parallelograms such as a rectangle, rhombus, or square, since they each have their own specific properties.