1.4 Key Concepts

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1.4 Key Concepts
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Angle

• Two different Rays with the same Endpoint

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Sides

• The Rays of the Angle

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Vertex

• The Endpoint of the Angle

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Acute Angle

• An Angle between 0 and 90 .

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Right Angle

• An Angle that equals 90

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Obtuse Angle

• An Angle between 90 and 180

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Straight Angle

• An Angle that equals 180

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Protractor Postulate

• The measure of an angle is equal to the absolute
  value of the difference between values of the
  rays on the protractor.

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Angle Addition Postulate

• If P is in the interior of ltRST, then mltRST
  mltRSP mltPST

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EXAMPLE 1
Name angles
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EXAMPLE 2
Measure and classify angles
SOLUTION
A protractor has an inner and an outer scale.
When you measure an angle, check to see which
scale to use.
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EXAMPLE 2
Measure and classify angles
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for Examples 1and 2
GUIDED PRACTICE
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for Examples 1and 2
GUIDED PRACTICE
2. Draw a pair of opposite rays. What type of
angle do the rays form?
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EXAMPLE 3
Find angle measures
SOLUTION
Angle Addition Postulate
Substitute angle measures.
145 6x 7
Combine like terms.
Subtract 7 from each side.
138 6x
Divide each side by 6.
23 x
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EXAMPLE 3
Find angle measures
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for Example 3
GUIDED PRACTICE
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for Example 3
GUIDED PRACTICE
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EXAMPLE 4
Identify congruent angles
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for Example 4
GUIDED PRACTICE
5. Identify all pairs of congruent angles in
the diagram.
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for Example 4
GUIDED PRACTICE
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EXAMPLE 5
Double an angle measure
SOLUTION
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for Example 5
GUIDED PRACTICE
7. Angle MNP is a straight angle, and NQ
bisects MNP. Draw MNP And NQ . Use
arcs to mark the congruent angles in your
diagram, and give the angle measures of these
congruent angles.