Geometry Notes T – 4: Exterior Angle Theorem
Definition: An exterior angle of a polygon is an angle outside the polygon formed by extending one side.
Theorem: The measure of an exterior angle of a triangle is equal to
Corollary: The measure of an exterior angle of a triangle is
Ex: Find the value of x in each diagram:
a.
b.
c.
a
c
b
3x
80
x
x
3x – 25
x
30
x
Exterior angle
a + b + c = 180 Interior angles of sum to 180
c + x = 180 Two adj. s that make a str. line are supp.
a + b + c = c + x Substitution
c = c Reflexive
a + b = x Subtraction
the sum of the measures of the two
remote (not adjacent) interior angles.
greater than the measure of either of the
remote interior angles.
30 + 90 = x
x = 120
x + 80 = 3x
x = 40
x + x = 3x - 25
x = 25
