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  αβ=9 αγ=24 βδ=50 α+β+γ+δ=360  Row2Row1Row2 αβ=9 βγ=15 βδ=50 α+β+γ+δ=360  Row4Row1Row4 αβ=9 βγ=15 βδ=50 2β+γ+δ=369  Pivot:Row2Row4 αβ=9 2β+γ+δ=369 βδ=50 βγ=15  Row321 Row2Row3 αβ=9 2β+γ+δ=369 0.5γ1.5δ=234.5 βγ=15  Row421 Row2Row4 αβ=9 2β+γ+δ=369 0.5γ1.5δ=234.5 1.5γ0.5δ=199.5  Pivot:Row3Row4 αβ=9 2β+γ+δ=369 1.5γ0.5δ=199.5 0.5γ1.5δ=234.5  Row41.50.5 Row3Row4 αβ=9 2β+γ+δ=369 1.5γ0.5δ=199.5 1.3333δ=168  δ=1.33333333168=126 γ=1.5199.5+0.5δ=1.5199.5+0.5 126=91 β=2369γδ=236991126=76 α=9+β=9+76=67=67  α=67 β=76 γ=91 δ=126

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