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Angles in a polygon

Angles in a polygon. Polygon : A closed plane figure with 3 or more sides Regular Polygon : A polygon with all congruent sides and angles. Interior Angles : The angles at each vertex inside a polygon.

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Angles in a polygon

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  1. Angles in a polygon • Polygon: A closed plane figure with 3 or more sides • Regular Polygon: A polygon with all congruent sides and angles. • Interior Angles: The angles at each vertex inside a polygon

  2. Exterior Angles: Angles formed between any side of a shape and a line extended from the next side. Supplementary: Angles that add up to 180° . ( an interior angle and its adjacent exterior angle is supplementary) Complementary: Angles that add up to 90°. Sum of the measures of the interior angles of a convex polygon:180° ( n-2) Example: Find the sum of the angles in a regular pentagon

  3. Angles in a triangle • Sum of angles in a triangle: Adding all the angles in a triangle gives 180°. • Remote Interior angles of a triangle: The two non adjacent angles to the exterior angle. • Exterior angle inequality: An exterior angle of a triangle is greater than either of the remote interior angles.

  4. Examples • Four exterior angles of a pentagon measure 20°, 81°, 33°, and 152°. What is the measure of the of the fifth exterior angle?

  5. 2. Find the sum of the measures of the interior angles of a convex 22-gon. 3. What is m∠BCD?

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