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Measuring Angles

Measuring Angles. Angle – formed by two rays with the same endpoint . The rays are the sides of the angle. The endpoint is the vertex of the angle. Vocabulary. Acute angle – 0 < x < 90 Right angle – x = 90 Obtuse angle – 90 < x < 180 Straight angle – x = 180

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Measuring Angles

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  1. Measuring Angles Angle – formed by two rays with the same endpoint. The rays are the sidesof the angle. The endpoint is the vertexof the angle.

  2. Vocabulary • Acute angle – 0 <x < 90 • Right angle – x = 90 • Obtuse angle– 90 < x < 180 • Straight angle – x = 180 • Congruent angles– angles with the same measure

  3. Vocabulary Continued … • Vertical angles – two angles whose sides are opposite rays. • Adjacent angles – two coplanar angles with a common side, a common vertex, and no common interior points. • Complementary angles – two angles whose measures have a sum of 90. • Supplementary angles – two angles whose measures have a sum of 180.

  4. Postulate 1 – 7 Protractor Postulate • Let ray OA and ray OB be opposite rays in a plane. Ray OA, ray OB and all the rays with endpoint O that can be drawn on one side of line AB can be paired with the real numbers from 0 to 180 so that • a. Ray OA is paired with 0 and ray OB is paired with 180. • b. If ray OC is paired with x and ray OD is paired with y, then m < COD = lx – yl.

  5. Postulate 1-8Angle Addition Postulate • If point B is in the interior of < AOC, then the m <AOB + m < BOC = m < AOC • If < AOC is a straight angle, then the m < AOB + m < BOC = 180.

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