Question

In a parallelogram of any two adjacent angle differ by 30 degree. find the measurements of all the amgles

Answer 1

lets consider a parallelogram ABCD where adjacent angles A, B are adjacent.

as the opposite angles in a parallelogram are equal,

angle A = angle C and angle B = angle D.

let angle A be x and angle B be y then

x-y = 30 ⇒x = 30+y

as the sum of all interior angles of a parallelogram is 360 degrees

x+y+angle C+angle D = 360

⇒x+y+x+y = 360 [∵angle C = x and angle D = y]

⇒2x+2y = 360

⇒2(30 +y)+2y = 360 [∵x = 30+y]

⇒60+2y+2y = 360

⇒4y = 360-60

⇒y = 300/4

⇒y = 75 then

angle A = y+30 = 75+30 = 105 degrees

angle B = y = 75 degrees

angle C = angle A = 105 degrees

angle D = angle B = 75 degrees