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Triangle Angle Sum Theorem, Triangle Exterior Angle Theorem

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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

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triangle angle sum theorem triangle exterior angle theorem
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
triangle angle sum theorem
Triangle Angle Sum Theorem

C

B

A

  • 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

exterior and remote interior angles
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
triangle exterior angle theorem
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

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