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Bellwork

Bellwork. If the measures of two angles of a triangle are 19 and 80, find the measure of the third angle Solve (x-2)180=1980 Find the value of x. x+3. 58. Section 8.1. Find Angle Measures in Polygons. The Concept. By this point we’ve already discussed the special properties of triangles

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Bellwork

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  1. Bellwork • If the measures of two angles of a triangle are 19 and 80, find the measure of the third angle • Solve (x-2)180=1980 • Find the value of x x+3 58

  2. Section 8.1 Find Angle Measures in Polygons

  3. The Concept • By this point we’ve already discussed the special properties of triangles • Now we’re going to discuss some special properties of polygons and then further these with special properties of polygons

  4. Definition Since we are discussing polygons that have more than three sides, we can now introduce the term… • Diagonal • Segment that joins two nonconsecutive vertices Axis of symmetry Vertex

  5. Theorems Theorem 8.1: Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex n-gon is (n-2)•180 Corollary to Theorem 8.1: Interior Angles of a Quadrilateral The sum of the measures of the interior angles of a quadrilateral is 360o. Axis of symmetry Vertex

  6. Example What is the sum of the interior angles of a decagon? Axis of symmetry Vertex

  7. Example Find the measure of the missing angle? 115 x 65 95 155 130 Axis of symmetry Vertex

  8. Theorems Theorem 8.2: Exterior Angles Theorem The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360o. Axis of symmetry Vertex

  9. No Clickers Example Find the measure of the missing angle? 65 x 115 25 85 50

  10. Practical Example The base of a jewelry box is shaped like a regular hexagon. What is the measure of each interior and exterior angle of the hexagon?

  11. Homework • 8.1 • 1, 2, 3-36 mult. 3

  12. Example Solve for x? 101 161 2x 95 163 3x+21 177

  13. Most Important Points • Definition of diagonal • Interior angles of a Polygon Theorem • Exterior angles of a Polygon Theorem

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