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1.3 Measuring Angles

1.3 Measuring Angles. Objectives: Measure angles with a protractor Identify and use the angle addition postulate. Warm-Up: Find the indicated value. AC = 20; AB = _____. A. B. C. x-4. 2x+3. Vocabulary:. Degree:. The most common unit of angle measure.

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1.3 Measuring Angles

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  1. 1.3 Measuring Angles Objectives: Measure angles with a protractor Identify and use the angle addition postulate Warm-Up: Find the indicated value. AC = 20; AB = _____ A B C x-4 2x+3

  2. Vocabulary: Degree: The most common unit of angle measure. (this is the unit of measure that results when a half circle is divided into 180 equal parts)

  3. Vocabulary: Protractor: A geometric ruler that is a half-circle with coordinates from 0oto 180o.

  4. Vocabulary: Measure of an Angles: m<AVB is |a – b| or |b – a| B A V

  5. Vocabulary: Complementary Angles: Two angles whose measures have a sum of 90o (each angle is called the compliment of the other) 67⁰ 60⁰ 23⁰ 30⁰

  6. Vocabulary: Supplementary Angles: Two angles whose measures have a sum of 180o (each angle is called the supplement of the other) 43⁰ 137⁰

  7. Vocabulary: Linear Pair: When the endpoint of a ray falls on a line so that two angles are formed, then the angles are known as a linear pair. 2 1 Linear Pair Property: If two angles form a linear pair they are supplementary.

  8. Vocabulary: Angle Congruence Postulate: If two angles have the same measure then they are congruent. If two angles are congruent then they have the same measure.

  9. Types of Angles: An angle whose measure is 90⁰ Right Angle: Acute Angle: An angle whose measure is less than 90⁰ An angle whose measure is greater than 90⁰ and less than 180⁰ Obtuse Angle:

  10. Vocabulary: Angle Addition Postulate: If point S is in the interior of <PQR the m < PQS + m < SQR = m < PQR S P R Q

  11. Example 1: Measure of an Angles: m<AVB is |a – b| or |b – a| m < BAC = ______ m < CAD = ______ m < BAD = ______ B C D A

  12. Example 2: Identify the Congruent Angles. A B D C

  13. Example 3: Name all the complementary and supplementary angle pairs. Complementary angles: ____ & _____ Supplementary angles: ____ & _____ 30o B 60o A 120o C

  14. Collins Writing Type 1: In creating a protractor, does the size of the half-circle make a difference?

  15. Example 4: Find the missing angle measures. m < BTE = 40⁰, m <ETM = 60⁰, m <BTM = ______ m < BTE = 112⁰, m <ETM = ______, m <BTM = 168⁰ m < BTE = ______, m <ETM = 47⁰, m <BTM = 92⁰ E B M T

  16. Example 5: m <XTY = 42⁰ and< WTX and <XTZ form a linear pair. Find the following: m < YTZ = ______ m <WTX = ______ m <WTY = ______ m <XTZ = ______ X Y W T Z

  17. Example 6: m < DSF = (45 + x)⁰, find the value of x and then give each indicated angle measure. m < DSF : m <DSE : m <ESF : D E (5x+4)⁰ S (4x+1)⁰ F

  18. Example 7: m < BAD = 82⁰& m <CAE = 64⁰ find: m < 1 : m <2 : m <3 : m <4 : m <BAF: B C 1 D 2 A 3 E 4 F

  19. Homework: pages 30-32 (21 problems) #’s 13-19, 27-34, 36-38, 42-44

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