In any parallelogram, the ratio of two adjacent angles is 1 : 5. Find

1.	In any parallelogram, the ratio of two adjacent angles is 1 : 5. Find the value of all angles of parallelogram.
Answer» Let ABCD is a parallelogram According to question ∠A : ∠B = 1 : 5 ∠A + ∠B = 180° ∵Sum of two adjacent angles of a parallelogram is 180° Sum of Ratio = 1 + 5 = 6 ∴∠A = 1/6 x 180° = 30° ∠B = 5/6 x 80° = 150° ∵ Opposite angles of a parallelogram are equal ∠C = ∠A = 30° and ∠D = ∠B = 150° ∴Angles of a parallelogram are 30°, 150°, 30° and 150°.

In any parallelogram, the ratio of two adjacent angles is 1 : 5. Find the value of all angles of parallelogram.

Answer»

Let ABCD is a parallelogram According to question

∠A : ∠B = 1 : 5

∠A + ∠B = 180°

∵Sum of two adjacent angles of a parallelogram is 180°

Sum of Ratio = 1 + 5 = 6

∴∠A = 1/6 x 180° = 30°

∠B = 5/6 x 80° = 150°

∵ Opposite angles of a parallelogram are equal

∠C = ∠A = 30°

and ∠D = ∠B = 150°

∴Angles of a parallelogram are 30°, 150°, 30° and 150°.