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The four angles of a quadrilateral form an AP. if the sum of the first three angles is twice the fourth angle then find all the angles

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∠A+∠B+∠C+∠D=360°[angle sum property of quadrilateral]

a-2d+a-d+a+d+a+2d=360

4a=360

a=90

∠A+∠B+∠C=2∠D

a-2d+a-d+a+d=2(a+2d)

3a-2d=2a+4d

a=6d

90=6d

15=d

∠A=a-2d=90-2×15=60°

∠B=a-d=90-15=75°

∠C=a+d=90+15=105°

∠D=a+2d=90+2×15=120°