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Measuring Angles

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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.

- 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

- 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.

- 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.

- 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.