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Aim: Exterior Angles Course: Applied Geo.
Aim: What’s outside the triangle?
Do Now:
Find the measure of angle z.
A
B
Cz470
360
Aim: Exterior Angles Course: Applied Geo.
83 + z = 180
47 + 36 + z = 180
x
Find the measure of angle z and x.
A
B
C Dz
z = 97
970
ACB and BCD are supplementary
97 + x = 180
830
The sum of the measure of the
angles of a triangle is 1800.
The sum of the measure of the
angles of a triangle is 1800.
830470
360
x = 83
47 + 36 = 83
Aim: Exterior Angles Course: Applied Geo.
z
C
E
ABC and CDE are supplementary
36 + z = 180
14401440
z = 144
A
B
470
360
970
47 + 97 = 144
remote interior angles
exterior angle
Aim: Exterior Angles Course: Applied Geo.
zCE
CAB and BAE are supplementary
47 + z = 180
1330
z = 133
A
B
470
360
970
36 + 97 = 133
remote interior angles
exterior angle
Aim: Exterior Angles Course: Applied Geo.
A
B
Cwy
x
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 + yExterior Angle
Theorem
Aim: Exterior Angles Course: Applied Geo.
Find the value of variable s
s0
130
128.50
s0 + 130 = 128.50
Exterior Angle Theorem
s0 = 115.50
so80o
50o50o 130o
Find the value of variable s
Isosceles triangle
Base angles of an isosceles triangle are congruent.
Aim: Exterior Angles Course: Applied Geo.
70
Model Problems
In the diagram, , and m 70,
and m 105, find m .
AB EF x
y z
���������������������������������������� ���
mQTS = mx = 70
105 = 70 + z
z
y
xA B
E T
Q
S T
R
alternate interior s
105 =
= 70
Exterior Angle Theorem 35 = z
F
35
Aim: Exterior Angles Course: Applied Geo.
52
3 14
Explain how you find m3 if m5 = 130 and m4 = 70.
m5 is an exterior angle of a triangle.Its measure equals the sum of m3 + m4, the remote interior angles of the triangle. Given that m5 = 1300 and m4 = 700,
m3 must be 600, the difference between m5 and m4.
Model Problems
= 130o
= 70o
Aim: Exterior Angles Course: Applied Geo.
xo
Model Problems
In the diagram, , and is
extended to point D. If m B and
m CAD 2 30, find .
AC BC BA
x
x x
50o
80o
2x + 30
Isosceles triangle
Base angles of an isosceles triangle are congruent.
xo
mDAC + mCAB = 180
AD
C
B
2x + 30 + x = 180 3x + 30 = 180
3x = 150 x = 50
50o130o
Aim: Exterior Angles Course: Applied Geo.
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.
x = smaller of two remote angles3x - 20 = larger of two
Exterior Angle Theorem
3x – 20 + x = 1204x – 20 = 120
4x = 140x = 35
= 35= 85
1200
1200 x
3x - 20
