Triangle Angle Sum Theorem, Triangle Exterior Angle Theorem

1
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

2
Triangle Angle Sum Theorem

• The sum of the measures of the angles of a
  triangle is 180.
• m?A m?B m?C 180

Ex If m?A 30 and m?B 70 what is m?C ?
m?A m?B m?C 180 30
70 m?C 180 100 m?C
180 m?C 180
100 80
3
Classifying Triangles
4
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

5
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