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Triangle Angle Sum Theorem, Triangle Exterior Angle
Theorem
Objectives
• State the triangle angle sum theorem and
solve for an unknown angle in a triangle
• Classify triangles based on measures of
angles as well sides
• State the triangle exterior angle theorem
and solve for an unknown exterior angle of
a triangle
1
Triangle Angle Sum Theorem
• The sum of the measures of the angles of
a triangle is 180°.
C
m∠A + m∠B + m∠C = 180
Ex: If m∠A = 30 and m∠B = 70;
what is m∠C ?
B
A
m∠A + m∠B + m∠C = 180
30 + 70 + m∠C = 180
100 + m∠C = 180
m∠C = 180 – 100 = 80
2
Classifying Triangles
3
Exterior and remote interior angles
• An exterior angle of a polygon
is an angle formed by a side
and an extension of an
adjacent side
• For each exterior angle of a
triangle, the two nonadjacent
interior angles are called the
remote interior angles
4
Triangle Exterior Angle Theorem
• The measure of each
exterior angle of a triangle
equals the sum of the
measures of its two remote
interior angles
m∠1 = m∠2 + m∠3
Ex: If m∠2 = 45 and m∠3 =
55, what is m∠1?
m∠1 = 45 + 55 = 100
5
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