Question

if the ratio of two adjacent angle of a parallelogram is 5:7 find the angles of parallelogram​

Answer 1

Total = (5+7) = 12

5/12 x 360

= 150 degrees

7/12 x 360

= 210 degrees

The four angles:

75, 75, 105 and 105 degrees.

Answer 2

Let ABCD be the given parallelogram.

$∠A : ∠B = 5:7 or \: \frac{∠A}{∠B} = \frac{5}{7} \\ \\ So \: \frac{∠A}{5} = \frac{∠B}{7} = x \\ \\ ∠A \: = 5x \: and \: ∠B = 7x \\ \\ Since \: two \: consecutive \: angles \: are \: supplementary, \\ \\ ∠A +∠B = 180 °\\ \\ 5x \times 7x = 180° \\ \\ ∠A = 5x = 5 \times 15°=75° \: \\ ∠B = 7x \times 15° = 105°. \\ \\ Since \: opposite \: angles \: of \: a \: Parallelogram \: are \:equal,\\ \\ ∠C=∠A=75° \\ ∠D=∠B =105°$