1-4: Measuring Angles

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1-4 Measuring Angles
2
Parts of an Angle

• An angle is formed by two rays with
  the same endpoint.
• The rays are the sides of the angle and the
  endpoint is the vertex of the angle.
• The interior of an angle is the
  region containing all points
  between the sides of the angle.
• The exterior of an angle is the region containing
  all points outside the angle.

3
Naming an Angle

• You can name an angle by its vertex (?A), a point
  on each ray and the vertex (?BAC or ?CAB), or a
  number (?1).
• Note When using 3 points to name an angle, the
  vertex must go in the middle!

4
Naming Angles

• What are two other names for ?1?
• What are two other names for ?KML?

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Measuring Angles

• One way to measure the size of
  an angle is in degrees.
• To say that the measure of ?A
  is 62?, you would write m?A 62?.
• Protractor Postulate Consider OB and point A 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.

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Types of Angles

• You can classify angles according to their
  measures.

Symbol for right angle!
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Measuring and Classifying Angles

• What are the measures of ?LKN, ?JKL, and ?JKN?
• Classify each as acute, right, obtuse, or
  straight.

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Congruent Angles

• Angles with the same measure are congruent
  angles.
• This means that if m?A m?B, then
  ?A ? ?B (and vice versa).
• You can mark angles with arcs to show they are
  congruent.

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Using Congruent Angles

• Synchronized swimmers form angles with their
  bodies.
• If m?GHJ 90?,
  what is m?KLM?
• If m?ABC 49?,
  what is m?DEF?

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? Which angle is congruent to ?WBM?
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Angle Addition

• Angle Addition Postulate If point B is in the
  interior of ?AOC, then
  m?AOB m?BOC m?AOC.

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Using the Angle Addition Postulate

• If m?RQT 155?, what are m?RQS and m?TQS?

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? If m?ABC 175?, what are m?ABD and m?CBD?