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An exterior angle of a polygon is an angle outside the polygon formed by one of its sides and the extension of an adjacent side. The sum of the measures of the interior angles of a polygon with n sides is n 2 180.

Triangle Angle Sum Exterior Angle Theorems Doodle Graphic

The sum of the measures of the exterior angles of a polygon one at each vertex is 360.

Find measure of exterior angle. The angles of a regular polygon are equivalent and their sides are as well. The 71 degree angle that we just found forms a linear pair with the exterior angle. Note that here i m referring to the angles w x and y as shown in the first image of this lesson.

We can subtract 71 from 180 to find the measure of the exterior angle. 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. To solve we use the fact that w x y.

If you count one exterior angle at each vertex. This means that these two angles must add up to 180 degrees. The sum of the exterior angles of a regular polygon will always equal 360 degrees.

Remember this formula for the number of sides n sum of internal angles of a regular polygon 2x n 2 x90 degree each interior angle of a regular polygon 2x n 2 x90 degree n each exterior. If the measure of the exterior angle is 3x 10 degrees and the measure of the two remote interior angles are 25 degrees and x 15 degrees find x. Measure of a single exterior angle formula to find 1 angle of a regular convex polygon of n sides.