Question

two adjacent angles of a parallelogram are in the ratio 1:5. find all the angles of the parallelogram.

Answer 1

let the angles be x and 5x
so in a parallelogram sum of adjacent angles=180degree
=x+5x=180
=6x=180
=x=30
5x=5*30=150
therefore the angles are 30deg, 150deg, 30deg and 150deg respectively(opposite angles in a parallelogram are equal)

Answer 2

Given,

The two adjacent angles of a parallelogram are in the ratio 1:5.

To find,

All the angles of the parallelogram.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the two adjacent angles of a parallelogram are x° and 5x°, respectively.

Mathematically,

The opposite angles of any parallelogram are equal.

Also, any two consecutive, adjacent angles of a parallelogram are supplementary.{Statement-1}

Now, according to the statement-1;

Sum of any two adjacent angles of a parallelogram = 180°

=> x° + 5x° = 180°

=> 6x° = 180°

=> x = 30

So the two adjacent angles of the parallelogram

two adjacent angles of the parallelogram are x° and 5x°, that is, 30° and 150°, respectively.

Now, according to statement-1,

As opposite angles of a parallelogram are equal

=> the four angles of the parallelogram are 30°, 30°, 150°, and 150°, respectively.

Hence, the four angles of the parallelogram are 30°, 30°, 150°, and 150°, respectively.