# Interior Angle

Pronunciation: /ɪnˈtɪər.i.ər ˈæŋ.gəl/ Explain

1

 Figure 1: Interior angle of a polygon.

The interior angle of a polygon is the angle on the interior at a vertex of the polygon.[2] Note that the sum of the measure of an interior angle of a polygon and the measure of the corresponding exterior angle is 180° or π radians.

2

 Figure 2: Interior angle between parallel lines.

When two parallel lines are intersected by a third line, the angles on the inside of the parallel lines are the interior angles. Note that the sum of the measure of the interior angle and the measure of the corresponding exterior angle is 180° or π radians.

### References

1. interior angle. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 8/7/2018. http://www.merriam-webster.com/dictionary/interior angle. Buy the book
2. Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid. pp 8,28-29. Translated by Casey, John, LL.D. F.R.S.. www.archive.org. Hodges, Figgis & Co.. 1890. Last Accessed 8/7/2018. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/8/mode/1up/search/interior. Buy the book
3. Williams, Cora Lenore. Syllabus of Plane Geometry. pg 14. www.archive.org. Standard Press. 1905. Last Accessed 8/7/2018. http://www.archive.org/stream/syllabusofplaneg00willrich#page/14/mode/1up/search/interior. Buy the book
4. Noetling, William. Elements of Constructive Geometry, Inductively Presented. pg 13. www.archive.org. Silver, Burdett & Company. 1897. Last Accessed 8/7/2018. http://www.archive.org/stream/elementsofconstr00noetrich#page/13/mode/1up/search/interior. Buy the book

• McAdams, David E.. Polygon. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. http://www.allmathwords.org/en/p/polygon.html.

McAdams, David E. Interior Angle. 4/23/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/interiorangle.html.

### Revision History

4/23/2019: Updated equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
8/6/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)