Answer. In solving equation there is only one value in solving an X.

Recall that the sum of the measure of the angles in a polygon with n sides is (n – 2)*180°. If the angles of a given polygon are given in terms of x, it is possible to find the value of x by using this formula. The number of sides that the polygon has is given, so first plug that value into the formula (n – 2)*180°.

Again, the formula for a regular polygon is 1/2 times the apothem multiplied by the perimeter. The perimeter is just the length of one side multiplied the by the number of sides (n); for a regular polygon, n also represents the number of triangles that make up the figure.

The formula for finding the total measure of all interior angles in a polygon is: (n – 2) x 180. In this case, n is the number of sides the polygon has. Some common polygon total angle measures are as follows: The angles in a triangle (a 3-sided polygon) total 180 degrees.

Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal. In this example, these are two pairs of Alternate Interior Angles: c and f.

When a transversal intersects two lines, the two lines are parallel if and only if interior angles on the same side of the transversal and exterior angles on the same side of the transversal are supplementary (sum to 180°).

Same-side interior angles are NOT always congruent. In fact, the only time they are congruent (meaning they have the same measure) is when the…

In other words, two lines are parallel when the interior angles on the same side sum to exactly 180 degrees.

180°

Co-interior angles lie between two lines and on the same side of a transversal. In each diagram the two marked angles are called co-interior angles. If the two lines are parallel, then co-interior angles add to give 180o and so are supplementary.

Two angles are Adjacent when they have a common side and a common vertex (corner point) and don’t overlap.

Corresponding angles These are sometimes known as ‘F’ angles. The diagram below shows parallel lines being intersected by another line. The two angles marked in this diagram are called corresponding angles and are equal to each other. The two angles marked in each diagram below are called alternate angles or Z angles.

Alternate angles form a ‘Z’ shape and are sometimes called ‘Z angles’. a and b are adjacent angles. Adjacent angles add up to 180 degrees. (d and c, c and a, d and b, f and e, e and g, h and g, h and f are also adjacent).

To find the value of a given exterior angle of a regular polygon, simply divide 360 by the number of sides or angles that the polygon has. For example, an eight-sided regular polygon, an octagon, has exterior angles that are 45 degrees each, because 360/8 = 45.

You need to know four things. the sum of all exterior angles equal 360, allexterior angles are the same, just like interior angles, and one exterior angle plus one interior angle combine to 180 degrees. Finally, the sum of interior angles is found with the formula 180(n-2) where n is the number of angles.