Eros2553
Eros2553 Eros2553
  • 13-09-2020
  • Mathematics
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Explanation & Process Needed

Explanation amp Process Needed class=

Respuesta :

jimrgrant1 jimrgrant1
  • 13-09-2020

Answer:

∠ BOF = 32°

Step-by-step explanation:

Since AB is a straight line, then

∠ AOE + ∠ EOD + ∠ DOE = 180° , substitute values

90 + x + 8 + 2x - 8 = 180 , that is

3x + 90 = 180 ( subtract 90 from both sides )

3x = 90 ( divide both sides by 3 )

x = 30

Thus

∠ DOB = 2x - 8 = 2(30) - 8 = 60 - 8 = 52°

∠ COF = 4x - 24 = 4(30) - 24 = 120 - 24 = 96°

∠ AOC = ∠ DOB ( vertical angles ), thus

y = 52, then

∠ BOF = 180° - (96 + 52)° = 180° - 148° = 32° ( angles on a straight line )

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