1. The sum of the measure of the angles of a triangle is 1800.
Find the measure of angle z and x. B
= 83
The sum of the measure of the angles of a triangle is 1800.
470
360
830
970 z
830 x A C D
z = 180
83 + z = 180
z = 97
ACB and BCD are supplementary
97 + x = 180
x = 83

2. remote interior angles
exterior angle E A B
470
360
970
1440
1440 z
= 144 C
ABC and CDE are supplementary
36 + z = 180
z = 144

3. remote interior anglesB
470
360
970
exterior angle
1330 z E C
= 133
CAB and BAE are supplementary
47 + z = 180
z = 133

4. Exterior Angle TheoremB
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

5. Exterior Angle Theorem
Find the value of variable s
130
128.50
Exterior Angle Theorem s0
s =
s0 =
Find the value of variable s
50o
130o
80o so
50o
Isosceles triangle
Converse of the Base angles of an
isosceles triangle are congruent.

6. Exterior Angle Theorem
Model Problems
= 70
105 = 35 70 F
mQTS = mx = 70
alternate interior s
105 = 70 + z
Exterior Angle Theorem
35 = z

7. Model Problems
Explain how you find m3 if m5 = 130 and m4 = 70. 5 2 3 1 4
= 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.

8. Model Problems C
80o
2x + 30
130o
50o xo
50o xo D A B
Isosceles triangle
mDAC + mCAB = 180
2x x = 180
3x + 30 = 180
3x = 150
x = 50
Base angles of an isosceles triangle are congruent.

9. Exterior Angle Theorem
The measure of an exterior angle of a triangle is 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
= 35
3x - 20 = larger of two
= 85
3x – 20 + x = 120
1200
4x – 20 = 120
4x = 140
x = 35