Math (4th Quarter Exam Reviewer)

• Angle


  Geometric figure formed by joining two rays at their endpoints. The vertex is the point where the rays meet, and the sides are the rays making up an angle.
• Angle measure


  Rotation or opening between the sides of an angle, measured in degrees (°) or radians
• Classifications of angles by measure


  • Acute (less than 90°)
  • Right (exactly 90°)
  • Obtuse (greater than 90° but less than 180°)
  • Straight (exactly 180°)
  • Reflex (greater than 180° but less than 360°)
• Acute angle

  Angle with measure less than 90°
• Right angle

  Angle with measure exactly 90°
• Obtuse angle


  Angle with measure greater than 90° but less than 180°
• Straight angle


  Angle with measure exactly 180°
• Reflex angle


  Angle with measure greater than 180° but less than 360°
• Angle Addition Postulate


  If a point O lies in the interior of ∠ABC, then m∠ABC = m∠ABO + m∠OBC
• Angle bisector


  Line, line segment, or ray that divides an angle into two equal parts
• Intersections of roads are often L-shaped (right angles) to minimize traffic when cars turn
• Angle bisector


  A line, line segment, or ray that bisects an angle; it divides the angle into two equal parts
• Angle bisector


  • ∠ADC is bisected by DB into congruent angles ∠ADB and ∠BDC
• Each of the two resulting angles from an angle bisector has a measure that is half of the measure of the original angle
• Angles


  • Acute angle: measure less than 90°
  • Right angle: measure exactly 90°
  • Obtuse angle: measure more than 90° but less than 180°
  • Straight angle: measure exactly 180°
  • Reflex angle: measure more than 180° but less than 360°
• Angle Addition Postulate


  1. Vertices of the individual angles must be the same

  2. Angles must share a common side
• If you add up marginal utility for each unit you get total utility
• Angle types in a triangle

  • Acute angles inside the triangle
  • Reflex angles outside the triangle
• Finding the angle formed when a triangular and square tabletop are joined


  Angle Addition Postulate: m∠ = 60° + 90° = 150°
• Angles in an isosceles triangle tent


  • Apex angle: 50°
  • Resulting angles from angle bisector: 25°
• An angle is a geometric figure formed by joining two rays at their endpoints
• The point where the rays meet is called the vertex, and the rays making up the angle are called the sides
• Congruent angles


  Angles with the same measure
• An angle measurement is the rotation or opening between the sides of an angle
• Angle bisector


  Line that divides an angle into two congruent parts
• Angles are classified according to their measurement
• The Angle Addition Postulate states that when two angles are placed side by side, their measures may be added to form a bigger angle
• Adjacent angles


  Angles that have the same vertex and a common side between them
• An angle bisector is a line, a line segment, or a ray that bisects or divides an angle into two equal parts
• Linear pair


  A pair of adjacent and supplementary angles
• When two lines intersect, they form angles that are adjacent and supplementary
• Vertical angles


  Nonadjacent angles formed when two lines intersect
• Vertical angles are equal to each other
• Supplementary angles


  Angles that add up to 180°
• The sum of the measures of a linear pair is 180°
• Statistics


  A branch of mathematics that deals with collecting, organizing, and interpreting data to address a certain phenomenon
• Population


  The set of all data under a study
• Sample


  The set of data drawn from the population
• Descriptive statistics


  • A branch of statistics that summarizes and describes important characteristics of the population or a sample
• Solving Example 4


  1. At 6:00 am, the hour and minute hands form a 180° angle

  2. For congruent angles, the second hand must bisect this angle at 90°

  3. The second hand will point to 3 (90°) 15 seconds after 6:00 am