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Warm Up

Warm Up. What is the sum of the interior angles of a triangle?. 2. What is the sum of the interior angles of the square?. 3 . Determine whether the figure is a polygon. Then state whether the polygon is convex or concave. Section 8.1 Angle Measures in Polygons. Recall….

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Warm Up

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  1. Warm Up • What is the sum of the interior • angles of a triangle? 2. What is the sum of the interior angles of the square? 3. Determine whether the figure is a polygon. Then state whether the polygon is convex or concave.

  2. Section 8.1Angle Measures in Polygons

  3. Recall… Discussion Diagonal – Is a segment that joins two nonconsecutive vertices. A triangle has no diagonals. Its interior angles add up to 180 degrees.

  4. Activity Discussion 1. Draw the polygon. heptagon 2. Choose one vertex and draw a diagonal. 5 3. Count how many triangles you have created. 4. What is the interior angles sum of each triangle? 180 5. What is the interior sum of the angles in the heptagon? 180 x 5 = 900

  5. Discussion What did you conclude???

  6. Theorem 8.1 : Polygon Interior Angles - The sum of the measures of the interior angles of a convex n-gon is 2 Where, n= number of sides, s= sum of interior angles 3 1 4

  7. Examples Find the sum of the measures of the interior angles of a: a) 15-gon b) 22-gon

  8. Examples Find the number of sides in each polygon a) 140 degrees b) 2340 degrees

  9. Examples Q 80° Solve for x. 114o R 70° xo 135o 70° P S 105o x 102o

  10. What about the exterior angles at each vertex??? 60 95 85 85 95 60 60

  11. What about the exterior angles at each vertex???

  12. Theorem 8.2 : Polygon Exterior Angles - The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360. 1 5 2 4 3

  13. Examples y a) Solve for y. 2y 2y y 72 b) Solve for angle 1 and 3. 1 3 70 68

  14. HomeworkWorkbook p.145#’s1-23 odd

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