Each Interior Angle Measure Equals Each Exterior Angle Measure

Each interior angle measure equals each exterior angle measure.

Each interior angle measure equals each exterior angle measure. You can put this solution on your website. Ea 36 degrees ia 144 degrees now the sum of the exterior angles of a polygon is always equal to 360 degrees. This tells us that the polygon is a regular polygon because all the interior angles are equal in measure.

Let be x degree the measure of an exterior angle then the measure of an interior angle is 2x degree. Assume that the regular polygon has n sides or angles. Each interior angle is equal to 4 times the exterior angle.

Interior angle exterior angle 180 8x x 180 9x 180 x 20 this means each exterior angle is 20 and each interior angle is 180 20 or 160. This means that ia ea 180 this means that 4x x 180 which means that 5x 180 which means that x 36 degrees which means that 4x 144 degrees. Ia interior angle ea exterior angle ie ea x then ia 4x now the interior angle of a polygon and its exterior angle are supplementary.

Substituting this value for x in the first equation we get. Find the measure of each angle. If one angle measures x degrees a second angle measures 3x degrees and a third angle measures 7x degrees express the measure of the fourth angle in terms of x.

We know that the sum of the interior angles is. Each exterior angle 360 number of vertices 360 9 40 degrees each interior angle 180 exterior angle 180 40 140 degrees. The measure of one interior angle of a parallelogram is 50 degrees more than 4 times the measure of another angle.

And the sum of exterior angles is. Since the number of angles is. The main idea behind the angle addition postulate is that if you place two angles side by side then the measure of the resulting angle will be equal to the sum.