Quadrilateral 81544

In the general quadrilateral ABCD, angle β is 9° greater than angle α, angle γ is 24° greater than angle α, and angle δ is 50° greater than angle β. Determine the sizes of individual angles.

Correct answer:

α =  67 °
β =  76 °
γ =  91 °
δ =  126 °

Step-by-step explanation:

β=9+α γ=24+α δ=50+β α+β+γ+δ=360  α−β=−9 α−γ=−24 β−δ=−50 α+β+γ+δ=360  Row2−Row1→Row2 α−β=−9 β−γ=−15 β−δ=−50 α+β+γ+δ=360  Row4−Row1→Row4 α−β=−9 β−γ=−15 β−δ=−50 2β+γ+δ=369  Pivot:Row2↔Row4 α−β=−9 2β+γ+δ=369 β−δ=−50 β−γ=−15  Row3−21​⋅ Row2→Row3 α−β=−9 2β+γ+δ=369 −0.5γ−1.5δ=−234.5 β−γ=−15  Row4−21​⋅ Row2→Row4 α−β=−9 2β+γ+δ=369 −0.5γ−1.5δ=−234.5 −1.5γ−0.5δ=−199.5  Pivot:Row3↔Row4 α−β=−9 2β+γ+δ=369 −1.5γ−0.5δ=−199.5 −0.5γ−1.5δ=−234.5  Row4−−1.5−0.5​⋅ Row3→Row4 α−β=−9 2β+γ+δ=369 −1.5γ−0.5δ=−199.5 −1.3333δ=−168  δ=−1.33333333−168​=126 γ=−1.5−199.5+0.5δ​=−1.5−199.5+0.5⋅ 126​=91 β=2369−γ−δ​=2369−91−126​=76 α=−9+β=−9+76=67=67∘  α=67 β=76 γ=91 δ=126

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