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r-ruslan [8.4K]
3 years ago
12

calculate the angles of a triangle if the angle alpha is 16 ° greater than the angle beta and the angle gamma is 52 ° smaller th

an the beta GIVING BRANLIEST***​
Mathematics
1 answer:
lakkis [162]3 years ago
4 0

Answer:

  • 88°, 72°, 20°

Step-by-step explanation:

<u>Angle alpha is 16° greater than the angle beta:</u>

  • α = β + 16°

<u>Angle gamma is 52° smaller than the beta:</u>

  • γ = β - 52

<u>Sum of angles is 180°, substitute α and β:</u>

  • α + β + γ = 180°
  • β + 16° + β + β - 52° = 180°
  • 3β - 36° = 180°
  • 3β = 216°
  • β = 216°/3
  • β = 72°

<u>Then</u>

  • α = 72° + 16° = 88°
  • γ = 72° - 52° = 20°
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