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