Question

The two a angles of a parallelogram are in ratio 7:2.find all the angles of the parallelogram

Answer 1

Correction in the question : The question should be "The two adjacent angles of a parallelogram are in ratio 7:2.find all the angles of the parallelogram".

SOLUTION :

Given,

Two angles of parallelogram are in ratio = 7:2

Sum of two adjacent angles in a parallelogram is 180°

Let the ratio of the angle be x

According to the problem,

7x + 2x = 180°

9x = 180°

x = 180/9

x = 20

Substitute x

One angle = 7x = 7(20) = 140°

Another angle = 2x = 2(20) = 40°

In a parallelogram the opposite angles are equal.

Therefore, the angles of parallelogram are 140°, 140°, 40° and 40°.

Answer 2

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

So, Angles of the given parallelogram measures 140°, 40°, 140°, 40°

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

Given :-

In a parallelogram

Ratio of adjacent angles = 7 : 2

To find : Measure of all angles in a Parallelogram

Solution :-

Ratio of adjacent angles = 7 : 2

Consider adjacent angles of Parallelogram as (7x)° and (2x)°

We know that in a Parallelogram adjacent angles are supplementary i.e, sum of adjacent angles equals to 180°

So, Equation formed : $\tt{\boxed{7x + 2x = 180}}$

$\tt{\implies{9x= 180}}$

$\tt{\implies{x = \dfrac{180}{9} }}$

$\tt{\implies{x = 20}}$

One angle = (7x)° = (7(20))° = 140°

Another angle = (2x) = (2(20))° = 40°

Another pair of angles measures 140° and 40° [Because Opposite angles in a parallelogram are equal]

So, Angles of the given parallelogram measures 140°, 40°, 140°, 40°

$\mathfrak{\large{\underline{\underline{More\:about\:Parallelogram:-}}}}$

What is a parallelogram ?

If both pairs of opposite sides of a quadrilateral are parallel such a quadrilateral is called a parallelogram.

Properties of Parallelogram :-

1) A diagonal of a parallelogram divides it into two congruent triangles.

2) Opposite sides of a parallelogram are equal and parallel.

3) Opposite angles in a parallelogram are equal.

4) Adjacent angles in a parallelogram are supplementary i.e, sum of angles is equal to 180°.