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Angles

Angles. KHM. Polygons. Definition:. A closed figure formed by a finite number of coplanar segments so that each segment intersects exactly two others, but only at their endpoints. These figures are not polygons. These figures are polygons. Interior Angle of a Polygon.

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Angles

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  1. Angles KHM

  2. Polygons Definition: A closed figure formed by a finite number of coplanar segments so that each segment intersects exactly two others, but only at their endpoints. These figures arenot polygons These figures are polygons

  3. Interior Angle of a Polygon The interior angles of a polygon are the angles inside the polygon, formed by two adjacent sides. For example, ∆ABC has interior angles:  ABC,  BAC,  BCA

  4. Exterior Angle of a Polygon An exterior angle of a polygon is an angle that forms a linear pair with an interior angle. It is an angle outside the polygon formed by one side and one extended side of the polygon. For example, ∆ABC has exterior angle:  ACD. It forms a linear pair with  ACB. Exterior Angle Interior Angles A D B C

  5. What is the sum of the measures of the interior angles of a convex n-gon?

  6. What is the sum of the measures of the exterior angles of a 3-gon? (a triangle) Sum of Measures of Exterior Angles = 360

  7. What is the measure of each exterior angle of a regular 3-gon? ? ? ?

  8. What is the measure of each exterior angle of a regular 4-gon? ? ? ? ?

  9. Angles made with parallel lines When a straight line crosses two parallel lines eight angles are formed. a b d c e f h g Which angles are equal to each other?

  10. Corresponding angles There are four pairs of corresponding angles, or F-angles. a a b b d d c c e e f f h h g g d = h because Corresponding angles are equal

  11. Corresponding angles There are four pairs of corresponding angles, or F-angles. a a b b d d c c e e f f h h g g a = e because Corresponding angles are equal

  12. Corresponding angles There are four pairs of corresponding angles, or F-angles. a b d c c e f h g g c = g because Corresponding angles are equal

  13. Corresponding angles There are four pairs of corresponding angles, or F-angles. a b b d c e f f h g b = f because Corresponding angles are equal

  14. Alternate angles There are two pairs of alternate angles, or Z-angles. a b d d c e f f h g d = f because Alternate angles are equal

  15. Alternate angles There are two pairs of alternate angles, or Z-angles. a b d c c e e f h g c = e because Alternate angles are equal

  16. Angles in a triangle c a b For any triangle, a + b + c = 180° The angles in a triangle add up to 180°.

  17. Calculating angles in a triangle Calculate the size of the missing angles in each of the following triangles. 64° b 116° 33° a 326° 31° 82° 49° 43° 25° d 88° c 28° 233°

  18. Interior and exterior angles in a triangle c b Any exterior angle in a triangle is equal to the sum of the two opposite interior angles. c a b a = b + c We can prove this by constructing a line parallel to this side. These alternate angles are equal. These corresponding angles are equal.

  19. Interior and exterior angles in a triangle

  20. Calculating angles Calculate the size of the lettered angles in each of the following triangles. 116° b 33° a 82° 64° 34° 31° 43° c 25° d 131° 152° 127° 272°

  21. Calculating angles Calculate the size of the lettered angles in this diagram. 38º 38º 56° 73° 86° a b 69° 104° Base angles in the isosceles triangle = (180º – 104º) ÷ 2 = 76º ÷ 2 = 38º = 86º Angle a = 180º – 56º – 38º = 69º Angle b = 180º – 73º – 38º

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