Quadrilateral and angles

In a quadrilateral, angle α is twice as large as angle β. Angle γ is 80% of angle α, and angle δ is 30° greater than angle α. Determine the angles of this quadrilateral.

Final Answer:

α =  68.75 °
β =  137.5 °
γ =  55 °
δ =  98.75 °

Step-by-step explanation:

r=80%=10080​=54​=0.8 α+β+γ+(30+α)=360 β=2⋅ α γ=r⋅ α  α+2⋅ α+r⋅ α+(30+α)=360 α+2⋅ α+0.8⋅ α+(30+α)=360  4.8α=330  α=4.8330​=68.75  α=4275​=68.75=68.75∘=68°45′
β=2⋅ α=2⋅ 68.75=137.5∘=137°30′
γ=r⋅ α=0.8⋅ 68.75=55∘
δ=30+α=30+68.75=98.75∘=98°45′

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