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If the sum of the interior angle of a polygon equals 4320 degrees what is the measure of each interior angle of the polygon?
Im stuck on that too :/
What is the Exterior Angle Theorem for a Triangle?
An exterior angle of a triangle is equal in measure to the sum of the other two interior angles.
What is the measure of an interior angle for a regular ten-sided polygon?
144o. Sum of exterior angles of a polygon is 360o. Each exterior angle for a regular decagon is 360o / 10 = 36o. Exterior and interior angles are supplementary, that is sum to 180o. Therefore the interior angle of a regular decagon is 180o - 36o = 144o.
If there a formula for finding the measure of an interior angle of a regular polygon?
Yes there is. You find the sum of the interior angles and then divide by the number of angles. Since being regular tells us that every interior angle has the same measurement, this works.Now to find the sum of the interior angles, let n be the number of sides, the the sum is180 degrees (n-2)For example, a triangle has 3 sides so n is 3 and the sum of its interior angles is 180(3-2) or 180 degreesA square has 180(4-2) or 360 degrees as the sum of its interior angles.A regular pentagon has 180(5-2)=180(3) degrees as the sum of the interior angles.Back to the triangle, since the sum is 180 degree and there are 3 angles, each on has measure 60. Similarly for a square, 360 divided by 4 is 90 and each interior angle has measure 90.
What therom states The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles?
the exterior angle theorem
