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=(4−2)⋅ 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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