Angles & Angle Pairs

• 1. Acute angle90° > x > 0°
  2. Right anglex = 90°
  3. Obtuse angle180° > x 90°
• Vertical angles - formed when two lines intersect, their vertex is the same and they are not sharing a common side.
• Adjacent angles


  Have a common vertex and side but no common interior points
• Complementary angles


  The sum of all measures is 90°. (Ex. 30° + 60°)
• Supplementary angles

  The sum of all measures is 180°.
• If two angles are adjacent and supplementary, they are called a linear pair.
• The formula to determine the total measures of the interior angles is based on the number of sides.
• Total interior angle -$180(n-2)$
• To determine the missing angle of the polygon you must:

  1. Determine the total interior angle of the polygon: 180(5 - 2).
  2. Subtract the total of the given angles to the sum of the interior angles: (120 + 130 + 110 + 105) - 465 (total of all angles.)

  
• • Total interior angle - 180(n-2) (N = number of sides)
  • One interior angle - 180(n-2)
  • Determine the number of sides when interior angle is given: n = 360/180 - interior angle
  • Determine the number of sides when sum of the measures of interior angles is given: n = total of interior angles + 360/180
• • Right angle - less than 90°
  • Straight angle - 180°
  • Obtuse angle - greater than 90° but less than 180°
  • Acute angle - less than 90° greater than 0°
  • Reflex angle - greater than 180° less than 360°
  • Full revolution - 360°
• Opposite angles are the same.
• Symbol “∠” used to denote an angle.
• A square mark means 90° and a straight line is 180°