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10.2 Diagonals and Angle Measures

10.2 Diagonals and Angle Measures. Vocabulary. Diagonals and Angle Measure . What You'll Learn. You will learn to find measures of interior and exterior angles of polygons. Nothing New!. Diagonals and Angle Measure . Make a table like the one below. 1) Draw a convex quadrilateral.

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10.2 Diagonals and Angle Measures

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  1. 10.2 Diagonals and Angle Measures

  2. Vocabulary Diagonals and Angle Measure What You'll Learn You will learn to find measures of interior and exterior angles of polygons. Nothing New!

  3. Diagonals and Angle Measure Make a table like the one below. 1) Draw a convex quadrilateral. 2) Choose one vertex and draw all possible diagonals from that vertex. 3) How many triangles are formed? 1 4 2 quadrilateral 2(180) = 360

  4. Diagonals and Angle Measure 1) Draw a convex pentagon. 2) Choose one vertex and draw all possible diagonals from that vertex. 3) How many triangles are formed? 1 4 2 quadrilateral 2(180) = 360 2 5 3 pentagon 3(180) = 540

  5. Diagonals and Angle Measure 1) Draw a convex hexagon. 2) Choose one vertex and draw all possible diagonals from that vertex. 3) How many triangles are formed? 1 4 2 quadrilateral 2(180) = 360 2 5 3 pentagon 3(180) = 540 3 6 4 hexagon 4(180) = 720

  6. Diagonals and Angle Measure 1) Draw a convex heptagon. 2) Choose one vertex and draw all possible diagonals from that vertex. 3) How many triangles are formed? 1 4 2 quadrilateral 2(180) = 360 2 5 3 pentagon 3(180) = 540 3 6 4 hexagon 4(180) = 720 4 7 5 heptagon 5(180) = 900

  7. Diagonals and Angle Measure 1) Any convex polygon. 2) All possible diagonals from one vertex. 3) How many triangles? 1 4 2 quadrilateral 2(180) = 360 2 5 3 pentagon 3(180) = 540 3 6 4 hexagon 4(180) = 720 4 7 5 heptagon 5(180) = 900 n - 3 n n - 2 n-gon (n – 2)180

  8. Diagonals and Angle Measure In §7.2 we identified exterior angles of triangles. Likewise, you can extend the sides of any convex polygon to form exterior angles. 48° 57° 74° The figure suggests a method for finding the sum of the measures of the exterior anglesof a convex polygon. 72° 55° 54° When you extend n sides of a polygon, n linear pairs of angles are formed. The sum of the angle measures in each linear pair is 180. sum of measure of exterior angles sum of measures of linear pairs sum of measures of interior angles = – = n•180 – 180(n – 2) = 180n – 180n + 360 sum of measure of exterior angles = 360

  9. Diagonals and Angle Measure Java Applet

  10. Diagonals and Angle Measure End of Section 10.2

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