1 / 11

Chapter 8.1 Notes: Find Angle Measures in Polygons

Chapter 8.1 Notes: Find Angle Measures in Polygons. Goal: You will find interior and exterior angle measures in polygons. Properties of a Polygon In a polygon, two vertices that are endpoints of the same side are called consecutive vertices .

matthewbowen
Download Presentation

Chapter 8.1 Notes: Find Angle Measures in Polygons

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 8.1 Notes: Find Angle Measures in Polygons Goal: You will find interior and exterior angle measures in polygons.

  2. Properties of a Polygon • In a polygon, two vertices that are endpoints of the same side are called consecutive vertices. • A diagonal of a polygon is a segment that joins two nonconsecutive vertices.

  3. Finding Interior Angle Measures in Polygons • Theorem 8.1 Polygon Interior Angles Theorem: The sum of the measures of the interior angles of a convex n-gon is (n – 2)180.

  4. Corollary to Theorem 8.1 Interior Angles of a Quadrilateral: The sum of the measures of the interior angles of a quadrilateral is 360o. Ex.1: Find the sum of the measures of the interior angles of a convex octagon.

  5. 1. 2. The coin shown is in the shape of a regular 11- gon. Find the sum of the measures of the interior angles. The sum of the measures of the interior angles of a convex polygon is 1440°. Classify the polygon by the number of sides. decagon ANSWER ANSWER 1620° for Examples 1 and 2 GUIDED PRACTICE

  6. Ex.2: The sum of the measures of the interior angles of a convex polygon is 900o. Classify the polygon by the number of sides. Ex.3: Find the value of x in the diagram shown.

  7. Ex.4: In the diagram below, find and Ex.5: The sum of the measures of the interior angles of a convex polygon is 1440o. Classify the polygon by the number of sides.

  8. Finding Exterior Angle Measures in Polygons • Theorem 8.2 Polygon Exterior Angles Theorem: The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360o.

  9. Exterior Angle Sum Theorem Exterior Angle Sum TheoremIf a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360°.

  10. Ex.6: What is the value of x in the diagram shown? Ex.7: A convex hexagon has exterior angles with measures 34o, 49o, 58o, 67o, and 75o. What is the measure of an exterior angle at the sixth vertex?

  11. Ex.8: The trampoline shown is shaped like a regular dodecagon. Find (a) the measure of each interior angle, and (b) the measure of each exterior angle. Ex.9: A stop sign is shaped like a regular octagon. Find (a) the measure of each interior angle, and (b ) the measure of each exterior angle.

More Related