Aim: What’s outside the triangle?
Do Now:
Find the measure of angle z.
B
360
470
A
Aim: Exterior Angles
z
C
Course: Applied Geo.
Find the measure of angle z and x.
B
47 + 36 = 83
The sum of the
360
measure of the
angles of a triangle
830 is 1800.
470
x0
97z0 83
C
A
D
47 + 36 + z = 180
83 + z = 180
z = 97
ACB and BCD are supplementary
97 + x = 180
Aim: Exterior Angles
x = 83
Course: Applied Geo.
remote
interior
angles
E
B 144
z 00
144
360
470
A
exterior
angle
47 + 97 = 144
970
C
ABC and CDE are supplementary
36 + z = 180
z = 144
Aim: Exterior Angles
Course: Applied Geo.
remote
interior
angles
exterior
angle
E
B
360
133z 0 470
A
970
C
36 + 97 = 133
CAB and BAE are supplementary
47 + z = 180
z = 133
Aim: Exterior Angles
Course: Applied Geo.
B
x
y
w
C
A
An exterior angle of a triangle is an angle
formed by a side of the triangle and the
extension of another side of the triangle.
w is an exterior angle of triangle ABC
x & y are nonadjacent interior angles
often called remote interior angles
The measure of an exterior angle of a triangle is
equal to the sum of the measures of the two
nonadjacent interior angles.
Exterior Angle
Theorem
Aim: Exterior Angles
w=x+y
Course: Applied Geo.
Find the value of variable s
130
128.50
Exterior Angle
Theorem
s0
s0 + 130 = 128.50
s0 = 115.50
Find the value of variable s
80
so o
50o
50o
130o
Isosceles triangle
Base angles of an isosceles triangle are congruent.
Aim: Exterior Angles
Course: Applied Geo.
Model Problems
In the diagram, AB EF , and mx  70,
and my  105, find mz .
Q
x
A
105 =
y
z35
E
= 70
B
R
70
S
T
T
F
mQTS = mx = 70 alternate interior s
Exterior Angle
Theorem
105 = 70 + z
35 = z
Aim: Exterior Angles
Course: Applied Geo.
Model Problems
Explain how
you find m3
if m5 = 130
and m4 = 70.
5 = 130o
2
4 = 70o
3 1
m5 is an exterior angle of a triangle.
Its measure equals the sum of m3 + m4,
the remote interior angles of the triangle.
Given that m5 = 1300 and m4 = 700,
m3 must be 600, the difference between
m5 and m4.
Aim: Exterior Angles
Course: Applied Geo.
Model Problems
In the diagram, AC  BC , and BA is
extended to point D. If mB  x and
mCAD  2 x  30, find x .
C
80o
2x +
30o 50
130
50
xo o
xo
D
A
B
Isosceles triangle
mDAC + mCAB = 180
2x + 30 + x = 180
3x + 30 = 180
3x = 150 x = 50
Aim: Exterior Angles
Course: Applied Geo.
Base angles of an isosceles triangle are congruent.
The measure of an exterior angle of a
triangle is 1200. If the measure of one of the
remote angles is 200 less than three times the
other remote angle, find the measure of the
two remote angles.
Exterior Angle
Theorem
3x - 20
1200
x
x = smaller of two remote angles
3x - 20 = larger of two
3x – 20 + x = 120
4x – 20 = 120
4x = 140
x = 35
Aim: Exterior Angles
= 35
= 85
1200
Course: Applied Geo.