Glencoe Geometry

Glencoe Geometry

Interior and Exterior Angles TARGETS Learn to use Polygon Angle Sum Theorem to find the measures of the interior angles. Learn to use the exterior and remote interior angles to find he measure of the exterior angle. Shape Number of Sides Sum of interior angles Triangle Quadrilateral Pentagon Hexagon

Heptagon Octagon Nonagon Decagon Hendecagon Dodecagon N-gon 3 4 5 6 7 8 9 10 11

12 n 180 Find the Interior Angles Sum of a Polygon A. Find the sum of the measures of the interior angles of a convex nonagon. A nonagon has nine sides. Use the Polygon Interior Angles Sum Theorem to find the sum of its interior angle measures. (n 2) 180 = (9 2) 180 = 7 180 or 1260 n=9 Simplify.

Answer: The sum of the measures is 1260. Find the Interior Angles Sum of a Polygon B. Find the measure of each interior angle of parallelogram RSTU. Step 1 Find x. Since the sum of the measures of the interior angles is Write an equation to express the sum of the measures of the interior angles of the polygon. Find the Interior Angles Sum of a Polygon

Sum of measures of interior angles Substitution Combine like terms. Subtract 8 from each side. Divide each side by 32. Find the Interior Angles Sum of a Polygon Step 2 Use the value of x to find the measure of each angle. m R = 5x = 5(11) or 55

m S = 11x + 4 = 11(11) + 4 or 125 m T = 5x = 5(11) or 55 m U = 11x + 4 = 11(11) + 4 or 125 Answer: mR = 55, mS = 125, mT = 55, mU = 125 A. Find the sum of the measures of the interior angles of a convex octagon. A. 900 B. 1080

C. 1260 D. 1440 A. B. C. D. A B C D B. Find the value of x. A. x = 7.8 B. x = 22.2 C. x = 15

D. x = 10 A. B. C. D. A B C D Interior Angle Measure of Regular Polygon ARCHITECTURE A mall is designed so that five walkways meet at a food court that is in the shape

of a regular pentagon. Find the measure of one of the interior angles of the pentagon. Find the sum of the interior angle measures. (n 2) 180 = (5 2) 180 n=5 = 3 180 or 540 Simplify. Find the measure of one interior angle. A pottery mold makes bowls that are in the shape of a regular heptagon. Find the measure of one of the interior angles of the bowl. A. 130 B. 128.57 C. 140 D. 125.5

A. B. C. D. A B C D Find Number of Sides Given Interior Angle Measure The measure of an interior angle of a regular polygon is 150. Find the number of sides in the polygon. Use the Interior Angle Sum Theorem to write an equation to solve for n, the number of sides. S

(150)n 150n 0 = = = = 180(n 2) 180(n 2) 180n 360 30n 360 360 = 30n 12 = n

Interior Angle Sum Theorem S = 150n Distributive Property Subtract 150n from each side. Add 360 to each side. Divide each side by 30. Answer: The polygon has 12 sides. The measure of an interior angle of a regular polygon is 144. Find the number of sides in the polygon. A. 12 0% B

0% A D. 10 A B C 0% D D C. 11 A. B. C.

0% D. C B. 9 Find Exterior Angle Measures of a Polygon A. Find the value of x in the diagram. Find Exterior Angle Measures of a Polygon Use the Polygon Exterior Angles Sum Theorem to write an equation. Then solve for x. 5x + (4x 6) + (5x 5) + (4x + 3) + (6x 12) + (2x + 3) + (5x + 5) = 360

(5x + 4x + 5x + 4x + 6x + 2x + 5x) + [(6) + (5) + 3 + (12) + 3 + 5] = 360 31x 12 = 360 31x = 372 x = 12 Answer: x = 12 Find Exterior Angle Measures of a Polygon B. Find the measure of each exterior angle of a regular decagon. A regular decagon has 10 congruent sides and 10 congruent angles. The exterior angles are also congruent, since angles supplementary to congruent angles are congruent. Let n = the measure of each exterior angle and write and solve an equation. 10n = 360

Polygon Exterior Angle Sum Theorem n = 36 Divide each side by 10. Answer: The measure of each exterior angle of a regular decagon is 36. A. Find the value of x in the diagram. A. 10 B. 12 C. 14 D. 15 A.

B. C. D. A B C D B. Find the measure of each exterior angle of a regular pentagon. A. 72 B. 60 C. 45 D. 90 A.

B. C. D. A B C D

Recently Viewed Presentations

  • Bellingham Marina Fire March 30, 2012

    Bellingham Marina Fire March 30, 2012

    Image shows fire looking from west, taken after 2nd alarm units arrived, approximately 20-30 minutes after initial alarm. Picture taken from slip east of fire - looking west. Picture taken some time after 2nd alarm units arrived (20-30 minutes after...
  • INTERACTIVE WEATHER MAP for Butterfield Trail elementary School

    INTERACTIVE WEATHER MAP for Butterfield Trail elementary School

    Brandy Todd, Ashley Carr and Sarah Bracey Introduction to Education, EAST/EMPACTS Dr. Regina Ryel Thomason, Instructor Introduction Mrs. Conner's 2nd grade class at Butterfield Elementary School, in Fayetteville AR, is in need of an interactive weather map.
  • Evolution of Technical Writing at Microsoft

    Evolution of Technical Writing at Microsoft

    "You're trying to take something that can be described in many, many sentences and pages of prose, but you can convert it into a couple of lines of poetry and you still get the essence." --Satya Nadella, Microsoft CEO ......
  • Controlling as a Management Function

    Controlling as a Management Function

    * Comparing Performance to Standards The comparison of actual performance with desired performance establishes the need for action. * Taking Corrective Action Managers can choose among three courses of action Do nothing Correct actual performance Modify standard * Taking Corrective...
  • DNA Extraction  Outline  Purpose of DNA extraction  Review

    DNA Extraction Outline Purpose of DNA extraction Review

    DNA Extraction Outline Purpose of DNA extraction Review the main steps in the DNA extraction protocol and the chemistry involved in each step Purpose of DNA Extraction To obtain DNA in a relatively purified form which can be used for...
  • Steam Economy measures - Spray Engineering Devices

    Steam Economy measures - Spray Engineering Devices

    125- 140 bar A • 500 - 550°C with Reheat . 3. 140 - 175 bar A • 550 - 580°C with Reheat and Bagasse Drying ... With Condensing Turbine in Reheat Cycle. Efficiency. 38 - 45%. PROPOSED - INDIA...
  • The Spelling Shed

    The Spelling Shed

    tens. ones. 10/07/2019. Place Value Lesson 1. Talking Time: Brooke thinks the place value grid below shows the number six hundred. Brooke is correct - there are six 100s counters in the hundreds column. Therefore, the place value grid shows...
  • In Defense of Quasi-Experiments - Faculty Server Contact

    In Defense of Quasi-Experiments - Faculty Server Contact

    Interrupted Time Series Design. One site pre-post implementation: Prison violence study by Byrne. Interrupted time series with non-equivalent control group: roadside sobriety checks in Michigan vs Ohio