Question

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

Answer 1

let the angles be A(a-2d) B(a-d) C(a+d) D(a+2d)
∠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°

Answer 2

Answer:

Step-by-step explanation:

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