Question

Calculate the number of degrees of one exterior and one interior angle of a regular 34-gon

Answer 1

One interior angle would have a measure of 169.4° and one exterior angle would have a measure of 10.6°.

We first find the sum of the angles of the 34-gon.  This is done using the formula
(n-2)(180), where n is the number of sides:

(34-2)(180) = 32(180) = 5760

Now we divide this by 34, since there are 34 congruent angles in the shape:

5760/34 = 169.4

The measure of an exterior and interior angle together will make 180°, so the exterior angle is found by

180-169.4 = 10.6°