1 / 13

WARM UP

WARM UP. Find the measure of the supplement of a 92° angle. Evaluate (n – 2)180 if n = 12 Solve = 60. SOLUTIONS. 180° - 92° = 88° (12 – 2)180 = 1800 = 60 Multiply both sides by n 60 n = 360 Divide both sides by 60 n = 6. 5.7. Find Angle Measures in Polygons.

lindley
Download Presentation

WARM UP

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. WARM UP Find the measure of the supplement of a 92° angle. Evaluate (n – 2)180 if n = 12 Solve = 60

  2. SOLUTIONS 180° - 92° = 88° (12 – 2)180 = 1800 = 60 Multiply both sides by n 60 n = 360 Divide both sides by 60 n = 6

  3. 5.7 Find Angle Measures in Polygons

  4. VOCABULARY • Regular polygon: a polygon that has all congruent sides and angles. • Diagonal: A diagonal of a polygon is a segment that joins two nonconsecutive vertices. • Interior angles of a polygon: An angle formed by two sides of a polygon. The original angles are the interior angles of the polygon. • Exterior angles of a polygon: An angle created by extending side of the polygon outside the figure forming linear pairs with the interior angles.

  5. Theorem 5.16: Polygon Interior Angles Theorem The sum of the measure of the interior angles of a convex n-gon is (n – 2)180°. n = 6 Corollary : Interior Angles of Quadrilateral The sum of the measure of the interior angles of a quadrilateral is 360°.

  6. Theorem 5.17: Polygon Exterior Angles Theorem • The sum of the measures of the exterior angles of a convex polygon , one angle at each vertex , is 360 ° .

  7. ANSWER The sum of the measures of the interior angles of an octagon is 1080°. Example 1: Find the sum of angle measures in a polygon • Find the sum of the measures of the interior angles of a convex octagon. SOLUTION An octagon has 8 sides. Use the Polygon Interior Angles Theorem. (n – 2) 180° = Substitute 8 for n. (8 – 2) 180° = 6 180° Subtract. = 1080° Multiply.

  8. Example2:Find the number of sides of a polygon • The sum of the measures of the interior angles of a convex polygon is 1260°. Classify the polygon by the number of sides. • Use the Polygon Interior Angles Theorem to write an equation involving the number of sides n. Then solve the equation to find the number of sides. (n – 2)•180° = 1260° Polygon Interior Angles Theorem n – 2 = 7 Divide each side by 180°. n = 9 Add 2 to each side. The polygon has 9 sides. It is a nonagon. SOLUTION

  9. Example 3: Find an unknown interior angle measure • Find the value of x in the diagram shown. • The polygon is a quadrilateral. Use the Corollary to the Polygon Interior Angles Theorem to write an equation involving x. Then solve the equation. x°+ 108° + 121° + 59° = 360° Corollary 8.1 x°+ 288° = 360 ° Combine Like Terms. x° = 72° Solve for x. SOLUTION

  10. 360° 3x + 156 = 68 x = Example 4: Find unknown exterior angle measures SOLUTION Use the Polygon Exterior Angles Theorem to write and solve an equation. x° + 2x° + 89° + 67° = 360 ° Polygon Exterior Angles Theorem Combine like terms. Solve for x.

  11. Checkpoint • Find the sum of the measures of the interior angles of the convex decagon. • The sum of the measures of the interior angles of a convex polygon is 1620°. Classify the polygon by the number of sides. • Use the diagram at the right. N Find m ‘s K and L. J M K L

  12. Checkpoint Cont…. 4. A convex pentagon has exterior angles with measures 66°, 77°, 82°, and 62°. What is the measure of an exterior angle at the fifth vertex? 5. Find the measure of (a) each interior angle and (b) each exterior angle of a regular nonagon.

  13. Homework p. 300-301 #’s 2 – 36 (even)

More Related