if an angle of a //gm is fouth-fifth of its adjacent angle find the angle of the //gm
Answers
Consider ABCD as a parallelogram If ∠ A = x degree
We know that ∠ B is adjacent to A which can be written as 4/5 x degree .
Opposite angles are equal in a parallelogram . So , we get ∠ A = ∠ C = x degree and ∠ B = ∠ D = 4/5 x degree .
We know that the sum of all the angles of a parallelogram is 360 degree .
It can be written as ∠ A + ∠ B + ∠ C + ∠ D = 360 degree. By substituting the values in the above equation x + (4/5) x + x + (4/5) x = 360 degree
By addition we get
2x + ( 8/5 ) x = 360 degree
By taking the LCM as 5 ( 18/5 ) x = 360 degree .
By cross multiplication
x = (360 × 5)/18 On further calculation x = 100 degree .
By substituting the value of x
So we get ∠ A = ∠ C = x = 100 degree ∠ B = ∠ D = 4/5 x degree = ( 4/5 ) ( 100 degree ) = 80 degree .
Therefore, ∠ A = ∠ C = x = 100 degree and ∠ B = ∠ D = 80 degree