Quadrilateral angles in AP

The four angles of a quadrilateral form an arithmetic progression. If the common difference is 15°, then find all the angles.

Correct answer:

α =  67.5 °
β =  82.5 °
γ =  97.5 °
δ =  112.5 °

Step-by-step explanation:

s=(42) 180=360  α+β+γ+δ=s   d=15   β=α +d γ=α +2d δ=α +3d  α+(α+d)+(α+2d)+(α+3d)=s α+(α+15)+(α+2 15)+(α+3 15)=360  4α=270  α=4270=67.5  α=2135=67.5=67.5=67°30
β=α+d=67.5+15=82.5=82°30
γ=β+d=82.5+15=97.5=97°30
δ=γ+d=97.5+15=112.5=112°30



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