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4.2
Angle Measure of Triangles
Theorem 4.1 Triangle Sum Theorem: the sum of the measures of the angles of a triangle is
180°.
B
In ABC, mA  mB  mC  180 .
A
C
Corollary: a corollary to a theorem is a statement that can be proved easily using the
theorem.
Corollary to the Triangle Sum Theorem: the acute angles of a right triangle are
complimentary.
In ABC , if mC  90, then  mA  mB  90 .
B
A
C
Interior Angles: the three original angles are the interior angles.
Exterior Angles: When the sides of a triangle are extended other angles are formed. The
angles adjacent to the interior angles are exterior angles.
Theorem 4.2 Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal
to the sum of the measures of the two nonadjacent interior angles.
m1  mA  mB
B
1
A
C
Examples:
Find the missing angle measure.
B
93
A
43
C
Using the triangle sum theorem we know that, the sum of all three angles is 180°.
So, the third angle is 180° – 93° – 43° = 44°.
Find the m1.
A
C
58
1
72
B
Using the Exterior Angle Theorem, we know that m1 = 58° + 72° = 130°.