Triangle Sum Theorem
&
Exterior Angle Theorem
Work in groups to answer the questions.
Try your best.
1.
1 2 3
2.
4
5
3.
Name 2 pair of alternate interior angles
5 & 3
and
4 & 1
What is the sum of m1 + m2 + m3?
180°
If m4 = 65° and m5 = 50°, what is
m2?
65°
90
°
50
°
130
50°
°
40
°
40 50
°90°
°
40
°
4.
Find all the angle measures
Vocabulary
• Adjacent angles – angles that share a common vertex
and side
• Vertical angles – a pair of non-overlapping angles that
are opposite and congruent to each other when two lines
intersect
• Complementary angles – two angles whose sum of
angle measures equals 90 degrees
• Supplementary angles – two angles whose sum of
angle measures equals 180 degrees
• Congruent angles – angles whose angle
measurements are equal
continued . . .
• Axes – the vertical and horizontal lines that act as a
reference when plotting points on a coordinate plane
• Exterior angles of a triangle – angles that are outside
of a triangle between one side of a triangle and the
extension of the adjacent side
• Interior angles of a triangle – angles that are inside of
a triangle, formed by two sides of the triangle
• Transversal – a line that intersects two or more lines
• Angle-angle criterion for triangles – if two angles in
one triangle are congruent to two angles in another
triangle, then the measure of the third angle in both
triangles are congruent
Objectives---What we’ll learn…
• Find the measurement of a missing angle
by using Triangle Angle Sum Theorem.
• Find the measurement of a missing angle
by using Exterior Angle Theorem.
Triangle Sum Theorem
The sum of the angle measures in a triangle
equal 180°
1
3
2
1 + 2 + 3 = 180°
Isosceles Triangles
2 congruent sides
2 congruent base angles
Isosceles Triangles & Angle Sum Theorem
Base Angles are congruent.
W  H
E + W + H = 180o
E + 2(W) = 180o
Exterior Angle Theorem
The measure of an exterior angle in a
triangle is the sum of the measures of
the 2 remote interior angles
exterior
angle
remote
interior
angles
A = C + D
Exterior Angle Theorem
The measure of an exterior angle in a
triangle is the sum of the measures of
the 2 remote interior angles
remote
interior
angles
exterior
angle
2
1
3
4 = 1 + 2
4
Example 1 on Exterior Angle
Example 2 on Exterior Angle
an example with numbers
find x & y
82°
x = 68°
30°
x
y
y = 112°
X
60º
42º
y