Question

the measure of two adjacent angle of parellelogram are in the ratio of 3:7. find the measure of the parellelogram of each angles. ​

Answer 1

Answer:-

Given:

The measure of two adjacent angles of a parallelogram are in the ratio 3 : 7.

Let the angles be 3x , 7x.

We know that,

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

Hence,

→ 3x + 7x = 180°

→ 10x = 180°

→ x = 180/10

→ x = 18

Therefore,

• 1st angle = 3x = 3 * 18 = 54°

• 2nd angle = 7x = 7 * 18 = 126°.

We know that,

Opposite angles of a parallelogram are equal.

so, the measures of other angles are also 54° , 126°.

Therefore, the measures of all angles of the given parallelogram are 54° , 126° , 54° , 126°.

Answer 2

Given :-

• The measure of two adjacent angle of parellelogram are in the ratio of 3 : 7

To Find :-

• The measure of the parellelogram of each angles

Solution :-

Let the first angle be 3x

Let the second angle be 7x

We know that,

$\boxed{\sf Sum \: of \: two \: angles \: of \: a \: parallelogram = 180°}$

Then,

$:\implies\sf3x + 7x = 180°$

$:\implies\sf10x = 180°$

$:\implies\sf x = \frac{\cancel{180}}{\cancel{10}}$

$:\implies\sf x = 18$

Therefore :-

• First angle = 3x = 3 × 18 = 54°
• Second angle = 7x = 7 × 18 = 126°

We also know that,

$\boxed{ \sf Opposite \: angles \: of \: a \: parallelogram \: are \: equal}$

That's why, the measures of other angles are 54° and 126°.

Therefore, the measure of the parellelogram of each angles are 54°, 126°, 54°, 126°.