Question

Two adjacent angles of a parallelogram have equal measure . Find the measure of each of the angles of the parallelogram​

Answer 1

In parallelogram ABCD,

angleA =angleC= x

angleB=angleD= y

therefore,

x+y+x+y=360

2x+2y=360.........…...………(equ.1)

2(x+y)=360

x+y=180

x=180-y

putting value of x in equ. 1

Answer 2

It is given that: angle DAB = angle ADC

We know that, angles DAB and ADC are supplementary because they are co-interior angles.

Here, x+x=180°

2x=180°

x=(180/2)°=90°

=angle DAB = angle ADC

We also know that opposite angles of a parallelogram are supplementary,then,

angle DAB + angle BCD = 180°

90° + angle BCD = 180°

angle BCD = (180-90)°

angle BCD = 90°

Now, angle CBA = 90°

Hence, all the angles of this parallelogram are of 90°

Hope it helps you out!!!