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Triangles: Angle Sum &
Classifying Triangles
Tutorial 12b
The Triangle Angle-Sum Theorem
The interior angles of any triangle have a
sum of 180.
mA + mB + mC = 180
A
B
C
Example Problems: Find the missing angles.
x =180 – (117 + 33) =30 
117
x
33
z y
w
t
30
45
t = 60 
y = 88 
w = 60 
z = 92 
47
Exterior Angles of a Triangle
An exterior angle of a polygon is an angle
formed by a side and an extension of a side.
For each exterior angle of a triangle, the two
non-adjacent interior angles are called its
remote interior angles.
1
Remote Interior Angles are 2 and
3
3
1
Exterior Angle is
2
Exterior Angle Theorem
The measure of an exterior angle of a triangle
equals the sum of the measures of its two
remote interior angles.
m1 = m2 + m3
2
1
3
Corollary: Exterior Angle Theorem
The measure of an exterior angle of a triangle
is greater than the measure of either of its
remote interior angles.
m1 > m2 and m1 > m3
2
1
3
Classifying Triangles:
Equilateral
All sides congruent
By Side Lengths
Isosceles
At least two sides
congruent
Scalene
No sides congruent
Classifying Triangles: By Angle Measure
Acute
Equiangular
All angles acute
All angles congruent
Obtuse
Right
One obtuse angle
One right angle
If you cannot remember the types of angles click here.
Review
A little more about Right Triangles
• In a right triangle, the side opposite the right
angle is the longest side. It is the called the
hypotenuse.
• The other two sides are called the legs of a
right triangle. Side c is the hypotenuse,
a
c
b
and is the longest side.
Sides a and b are the legs
of the triangle.
Classifying Angles
Back
Types of Angles:
Acute Angle:
Angles less than 90° are
called Acute Angles.
Right Angle:
Obtuse Angle:
Angles greater than 90°
are called Obtuse Angles.
Straight Angle:
Symbol for right angle
180°
Angles equal to 90° are
called Right Angles.
Angles equal to 180° are
called Straight Angles.
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