1 / 11

Angles and Polygons

Angles and Polygons. 13.3. LESSON. Tambourines The frame of the tambourine shown is a regular heptagon. What is the measure of each angle of the heptagon?. Angles and Polygons. 13.3. LESSON.

nellie
Télécharger la présentation

Angles and 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. Angles and Polygons 13.3 LESSON Tambourines The frame of the tambourine shown is a regular heptagon. What is the measure of each angle of the heptagon?

  2. Angles and Polygons 13.3 LESSON An interior angle of a polygon is an angle inside the polygon. You can find the measure of an interior angle of a regular polygon by dividing the sum of the measures of the interior angles by the number of sides.

  3. Angles and Polygons 13.3 LESSON (n – 2) • 180˚ n The measure of an interior angle of a regular n-gon is given by the formula . Measures of Interior Angles of a Convex Polygon The sum of the measures of the interior angles of a convex n-gon is given by the formula (n – 2) • 180˚.

  4. Angles and Polygons 13.3 LESSON 1 EXAMPLE Finding the Sum of a Polygon’s Interior Angles Find the sum of the measures of the interior angles of the polygon. SOLUTION For a convex pentagon, n = 5. (n – 2) • 180˚ = (5 – 2)• 180˚ = 3 • 180˚ = 540˚

  5. Angles and Polygons 13.3 LESSON 1 EXAMPLE Finding the Sum of a Polygon’s Interior Angles Find the sum of the measures of the interior angles of the polygon. SOLUTION For a convex octagon, n = 8. (n – 2) • 180˚ = (8 – 2)• 180˚ = 6 • 180˚ = 1080˚

  6. Angles and Polygons 13.3 LESSON 2 EXAMPLE (n – 2) • 180˚ n (7 – 2) • 180˚ 7 Measure of an interior angle = = Finding the Measure of an Interior Angle Find the measure of an interior angle of the frame of the heptagonal tambourine. SOLUTION Because the tambourine is a regular heptagon, n = 7. Write formula. Substitute 7 for n. Evaluate. Use a calculator. ≈ 128.6˚ The measure of an interior angle of the frame of the tambourine is about 128.6˚. ANSWER

  7. Angles and Polygons 13.3 LESSON Exterior Angles When you extend a side of a polygon, the angle that is adjacent to the interior angle is an exterior angle. In the diagram, 1 and 2 are exterior angles. An interior angle and an exterior angle at the same vertex form a straight angle.

  8. Angles and Polygons 13.3 LESSON 3 EXAMPLE Finding the Measure of an Exterior Angle Find m1 in the diagram. SOLUTION The angle that measures 87˚ forms a straight angle with 1, which is the exterior angle at the same vertex. Angles are supplementary. m1 + 87˚ = 180˚ Subtract 87˚ from each side. m1 = 93˚

  9. Angles and Polygons 13.3 LESSON 4 EXAMPLE (6 – 2) • 180˚ 6 (6 – 2) • 180˚ 6 The measure of an interior angle of a regular hexagon is . + m2 = 180˚ Finding an Angle Measure of a Regular Polygon Teapots The diagram shows a teapot in the shape of a regular hexagon. Find m2. SOLUTION Angles are supplementary. m1 + m2 = 180˚ Substitute formula form1. Simplify. 120˚ + m2 = 180˚ Subtract 120˚ from each side. m2 = 60˚

  10. Angles and Polygons 13.3 LESSON Sum of Exterior Angle Measures Each vertex of a convex polygon has two exterior angles. If you draw one exterior angle at each vertex, then the sum of the measures of these angles is 360˚. The calculations below show that this is true for a triangle. m4 + m5 + m6 = (180˚ – m1) + (180˚ – m2) + (180˚ – m3) = (180˚ + 180˚ + 180˚) – (m1 + m2 + m3) = 540˚ – 180˚ = 360˚

  11. Angles and Polygons 13.3 LESSON 5 EXAMPLE Using the Sum of Measures of Exterior Angles Find the unknown angle measure in the diagram. SOLUTION Sum of measures of exterior angles of convex polygon is 360˚. x˚ + 81˚ + 100˚ + 106˚ = 360˚ Add. x + 287 = 360 Subtract 287 from each side. x = 73 ANSWER The angle measure is 73˚.

More Related