Question

In a quadrilateral ABCD, angle A, angle B, angle c, angle D are respectively in arithmetic progression and angle c =100.find the remaining three angles of quadrilateral.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

we know,

sum of all angles of a quadrilateral is 360.

let the 'd' be x

then,

A/Q

let the angles be

angle A = 100-2x

angle B = 100-x

angle C = 100(given)

angle D = 100+x

A/Q

(100-2x)+(100-x)+(100)+(100+x)=360

or,400-2x=360

or,2x=400-360

or,2x = 40

or,x = 20.

hence angles are

A= 100-2*20=100-40=60

B= 100-20= 80

D= 100+20=120

Proof, A+B+C+D = 360

60+80+100+120= 360

360= 360

proved.