Question

Two angles of parallelogram are in the ratio 5:7. if the bigger angle is halved , what will be the ratio of the angles of the new parallelogram obtained ?

pls answer correctly with steps

Answer 1

Answer:

7:17

Step-by-step explanation:

Given that 2 angles of the parallelogram are in the ratio 5:7.

Let the angles be 5k and 7k.

We also know that opposite angles in a parallelogram are equal.

So these 2 angles would be adjacent.

Also sum of 2 adjacent angles in a parallelogram are supplementary.

Hence, 5k + 7k = 12k = 180°

=> k = 15°

Thus the 2 angles are 5k = 75° and

7k = 105°.

Now given that the bigger angle is halved , hence it will be equal to 105/2°

Now, the other angle would be 180 - 105/2 = 255/2°

Now the ratio of 2 angles of the new parallelogram would be

105/2 : 255/2

=21 : 51

=7 : 17

(But notice that the bigger angle in the first parallelogram after having becme the smaller one)

Answer 2

Answer:

Ratio of angles in new parallelogram 7:17

Solution:

Given : Ratio of two angles of a parallelogram 5:7

To calculate:

if the bigger angle is halved , what will be the ratio of the angles of the new parallelogram obtained ?

As we know that sum of adjacent angles of a parallelogram are 180°,and opposite angles of a parallelogram are equal.

it is clear from the data that given angles are adjacent so

$5k + 7k = 180° \\ \\ 12k = 180° \\ \\ k = \frac{180°}{12} \\ \\ k = 15°$
So angles are

$15° \times 5 = 75° \\ \\ 15° \times 7 = 105°$

Now bigger angle had to be halved

$\frac{105°}{2} = 52.5° \\ \\ so \: other \: angle \: is \: \\ 180° - 52.5° = 127.5° \\ \\ ratio \: = \frac{52.5}{127.5} \\ \\ = \frac{7}{17}$

Hope it helps you.