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Understanding and Measuring Angles: An Introduction to Angle Types and Postulates

This educational content provides a comprehensive overview of angles, including their definitions, naming conventions, and properties. It explains how angles are formed by two rays with a common endpoint (the vertex) and details how to measure them using protractors and postulates like the Angle Addition Postulate. Learn to classify angles as acute, right, obtuse, or straight, and understand congruent angles. Through examples and practical applications, this resource serves as a foundation for mastering angle measurement and comparison.

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Understanding and Measuring Angles: An Introduction to Angle Types and Postulates

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  1. 1-4 Measuring Angles Objective: To find and compare measures of angles.

  2. Angles • Definition: formed by two rays with the same endpoint. The rays are the sides of the angle. The endpoint is the vertex of the angle. • How to Name it: its vertex, a point on each ray and the vertex, a number • Example: ∠B ∠ABC ∠CAB ∠1 A C 1 B

  3. Naming Angles What are the two other names for ∠1 and ∠2 ? L N 1 2 M P

  4. Postulate 1-7Ruler Postulate A O B Consider OB and a point on one side of OB. Every ray of the form OA can be paired one to one with a real number from 0 to 180.

  5. Protractor Postulate D C d c O The measure of ∠COD is the absolute value of the difference of the real numbers paired with OC and OD. That is, if OC corresponds with c, and OD corresponds with d, then m∠COD= | c – d| .

  6. Types of Angles Right Acute 0˚ < x < 90˚ x = 90˚ x = 180˚ Obtuse 90˚ < x < 180˚ Straight

  7. Measuring and Classifying Angles J M L H N What are the measures of ∠LKN, ∠NKM, and ∠JKN? Classify each angle as acute, right, obtuse, or straight.

  8. Congruent Angles When angles have the same measure, they are said to be congruent angles. 2 55˚ 55˚ 1 ∠1 ≅ ∠2 “angle 1 is congruent to angle 2” m∠1 = m∠2 “the measure of angle 1 is equal to the measure of angle 2

  9. Postulate 1-7Angle Addition Postulate If point Bis in the interior of ∠AOC, then m∠AOB+ m∠BOC= m∠AOC. A B O C

  10. Using the Angle Addition Postulate Find m∠SOPand m∠POT, when m∠SOT= 100˚. S P 2n + 4 3n - 19 O T

  11. Using the Angle Addition Postulate If m∠WXY= 160˚, what are m∠WXZand m∠ZXY? Z Y 7x - 4 5x + 8 W X

  12. Using the Angle Addition Postulate ∠DEF is a straight angle. What are m∠DECand m∠CEF? C 2x + 10 11x - 12 D F E

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