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In the figure, ∠6 is an exterior angle to (square) AUL.

A: Explain why m∠6 is equal to the sum of the measures of the two nonadjacent interior angles.
B: What is m∠6?
Answer:

In the figure 6 is an exterior angle to square AUL A Explain why m6 is equal to the sum of the measures of the two nonadjacent interior angles B What is m6 Answ class=

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mhanifa

Answer:

Part A

  • ∠6 + ∠3 = ∠PAL - angle addition
  • ∠PAL = 180° - straight angle
  • ∠6 + ∠3 = 180° - substitution
  • ∠6 = 180° - ∠3           (1)

ΔAUL has

  • ∠1 + ∠2 + ∠3 = 180° - property of triangles
  • ∠1 + ∠2 = 180° - ∠3     (2)

(1) and (2) have RHS same, therefore LHS also same:

  • ∠6 = ∠1 + ∠2

Part B

  • ∠6 = ∠1 + ∠2 - given

Substitute measures

  • ∠6 = 52° + 33°
  • ∠6 = 85°

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