A regular polygon has an exterior angle measure of (x+3) degrees and an interior angle measure of (13x-33) degrees. MEASURE OF EACH ANGLE      

Expert Answers

An illustration of the letter 'A' in a speech bubbles

A regular polygon has exterior angle measure `(x+3)^circ` and interior angle measure of `(13x-33)^circ` . Find the measure of each angle.

(1) Since the polygon is regular, each interior angle is congruent, as are the exterior angles.

(2) The interior angle and exterior angle at a vertex are supplementary, thus:

`13x-33+x+3=180`
`x=15`

(3) Then each interior angle is `162^circ` and each exterior angle is `18^circ`

** There are `(360)/(18)=20` sides, and the sum of the interior angles is `20*162=3240^circ` **

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial