Question

In a quadrilateral ABCD,angle A,angle B,angleC and angleD are respectively in AP and angleC=100°. Find the remaining three angles of quadrilateral

Answer 1

as the angles are in A.P

we can assume

angle A = a-3d

angle B = a-d

angle C =a+d

angle D = a+3d

as the fig. is a quadrilateral

ang. A + ang. B + ang. C + ang. D =360

i.e., (a-3d) + (a-d) + (a+d) + (a+3d)=360

4a=360

a=99

also, a+d =100

or, 90+d=100

hene, d= 10

angle A = a-3d= 90-3(10)= 60

angle B = a-d = 90-10= 80

angle C = a+d = 90+10 = 100

angle D = a+3d = 90 +3(10) = 120