Tracing all the way around the polygon makes one full turn , so the sum of the exterior angles must be 360°. is convex, then the sum of the measures of the exterior angles, one at each vertex, is In order to find the measure of a single interior angle of a regular polygon  (a polygon with sides of equal length and angles of equal measure) with n sides, we calculate the sum interior anglesor $$(\red n-2) \cdot 180$$ and then divide that sum by the number of sides or $$\red n$$. One Therefore, to sum the external angles, we can do n.360 - internal angles. m Now you are able to identify interior angles of polygons, and you can recall and apply the formula, S = (n - 2) × 180 °, to find the sum of the interior angles of a polygon. This question cannot be answered because the shape is not a regular polygon. The value 180 comes from how many degrees are in a triangle. 180 Use Interior Angle Theorem: + \frac{(\red8-2) \cdot 180}{ \red 8} = 135^{\circ} \$. Therefore, N = 180n – 180(n-2) N = 180n – 180n + 360. What is the measure of 1 interior angle of a regular octagon? Polygons come in many shapes and sizes. A polygon is a plane shape bounded by a finite chain of straight lines. 360° since this polygon is really just two triangles and each triangle has 180°, You can also use Interior Angle Theorem:$$(\red 4 -2) \cdot 180^{\circ} = (2) \cdot 180^{\circ}= 360 ^{\circ}$$. ° The exterior angle theorem tells us that the measure of angle D is equal to the sum of angles A and B.In formula form: m