Aim: What

1
Aim Whats outside the triangle?
Do Now
Find the measure of angle z.
B
z
A
C
2
Find the measure of angle z and x.
B
The sum of the measure of the angles of a
triangle is 1800.
47 36 83
830
x
z
970
A
C
D
47 36 z 180
83 z 180
z 97
?ACB and ?BCD are supplementary
97 x 180
x 83
3
E
z
1440
47 97 144
C
?ABC and ?CDE are supplementary
36 z 180
z 144
4
z
C
E
36 97 133
?CAB and ?BAE are supplementary
47 z 180
z 133
5
B
Exterior Angles
x
y
w
A
C
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. w x y
Exterior Angle Theorem
6
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
so
80o
50o
Isosceles triangle
Base angles of an isosceles triangle are
congruent.
7
Model Problems
70
105
70
35
F
m?QTS m?x 70
alternate interior ?s
105 70 z
Exterior Angle Theorem
35 z
8
Model Problems
Explain how you find m?3 if m?5 130 and m?4
70.
130o
70o
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.
9
Model Problems
C
80o
2x 30
50o
50o
130o
xo
xo
A
D
B
Isosceles triangle
m?DAC m?CAB 180
2x 30 x 180
3x 30 180
3x 150
x 50
Base angles of an isosceles triangle are
congruent.
10
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