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strojnjashka [21]
3 years ago
10

(Help) Find the measure of the missing angle

Mathematics
1 answer:
melisa1 [442]3 years ago
8 0

Solution:

Let the missing angle be x.

<u>It should be noted:</u>

  • The two diagonals form four isosceles triangles. (ΔBOC, ΔCOD, ΔDOA, and ΔAOB)
  • ∠DOA = ∠BOC = 44 (Vertically opposite angles)
  • Interior angles of a triangle sum up to 180°

<u>This means that...</u>

  • 44 + x + x = 180

<u>Combine like terms.</u>

  • 44 + 2x = 180

<u>Subtract 44 both sides.</u>

  • 2x = 180 - 44

<u>Simplify the RHS</u>

  • 2x = 136

<u>Divide 2 both sides.</u>

  • 2x/2 = 136/2
  • => x = 136/2 = 68°
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