Question

ABCD is a parallelogram. Find x and y and hence find all the angles of the parallelogram.

Answer 1

angle sum property of a parallelogram a is 360 degrees

thus

4x+2y+2x-3y+10+X+2y-10+3x+5y=360

10x+6y=360

Answer 2

Step-by-step explanation:

In parallelogram, the opposite angles are same...

so,

angle A= angle C and

angle B= angle D

x+2y-10=2x-3y+10 eq1

4x+2y=3x+5y. eq2

let's solve eq1

2y+3y=2x-x+10+10

5y=x+20

so x-5y=-20. eq3

similarly by solving eq2 we get

x-3y=0. eq4

now solve eq3 and eq4 by elimination method

and we get y=10

put the value of y in eq 3

we get x=30

now by putting the values of x and y in angles

we get angle A=angle C= 40

angle B= angleD= 140.