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.

Correct 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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