4.2 Angles of Triangles

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4.2 Angles of Triangles
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Objectives

• Apply the Angle Sum Theorem
• Apply the Exterior Angle Theorem

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Theorem 4.1 Angle Sum Theorem

• The sum of the measures of the angles of a
  triangle is 180.
• m?X m?Y m?Z 180

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Example 1
Find the missing angle measures.
Angle Sum Theorem
Simplify.
Subtract 117 from each side.
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Example 1
Angle Sum Theorem
Simplify.
Subtract 142 from each side.
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Your Turn
Find the missing angle measures.
Answer

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Theorem 4.2 Third Angle Theorem

• If two angles of one triangle are congruent to
  two angles of a second triangle, then the third
  angles of the triangle are congruent.
• Abbreviation If 2 ?s of one ? are ? to 2 ?s
  of another ?, then third ?s are ?.

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Exterior Angles and Triangles

• An exterior angle is formed by one side of a
  triangle and the extension of another side (i.e.
  ?1 ).
• The interior angles of the triangle not adjacent
  to a given exterior angle are called the remote
  interior angles (i.e. ?2 and ?3).

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Theorem 4.3 Exterior Angle Theorem

• The measure of an exterior angle of a triangle
  is equal to the sum of the measures of the two
  remote interior angles. m ?1 m
  ?2 m ?3

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Example 2
Find the measure of each numbered angle in the
figure.
Exterior Angle Theorem
Simplify.
If 2 ?s form a linear pair, they are
supplementary.
Substitution
Subtract 70 from each side.
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Example 2
Exterior Angle Theorem
Substitution
Subtract 64 from each side.
If 2 ?s form a linear pair, they are
supplementary.
Substitution
Simplify.
Subtract 78 from each side.
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Example 2
Angle Sum Theorem
Substitution
Simplify.
Subtract 143 from each side.
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Your Turn
Find the measure of each numbered angle in the
figure.
Answer

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Corollaries

• A corollary is a statement that can be easily
  proven using a theorem.
• Corollary 4.1 The acute ?s of a right ? are
  complementary.
• Corollary 4.2 There can be at most one right or
  obtuse ? in a ?.

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Example 3
Corollary 4.1
Substitution
Subtract 20 from each side.
Answer

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Your Turn
Answer

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Assignment

• Geometry Pg. 189 11 - 35
• Pre-AP Geometry Pg. 189 11 - 40