Question

the 4 angles of a quadrilateral are in arithmetic sequence.the smallest angle is 18 degree.find all the angles

Answer 1

Let the step of increase per progressive number be x.
⇒The numbers are $18,18+x,18+2x$ and $18+3x$ respectively.
We know ,
Sum of angles in a quadrilateral=360 degree.
⇒By the condition:
$18+18+x+18+2x+18+3x=360$
⇒$6x=360-72$
⇒$x= \frac{288}{6} =48$
⇒The angles are :
1>18 degree
2>18+48=66 degree
3>18+48*2=114 degree
4>18+48*3=162 degree.
Ans:The angles are 18 degree  , 66 degree  , 114 degree and 162 degree.

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