Question

the measure of two adjacent of a parallelogram are in the ratio 6: 4 . Find the measure of the eachof the angle of a parallelogram
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Answer 1

Given -

• Ratio of adjecent angles = 6 : 4

To find -

• Measure of each angles.

Formula used -

• Angle sum property of parallelogram.

Solution -

In the question, we are provided with the ratio of adjecent sides of a parallelogram, and we need to find the measure of each angle. As we know that opposition sides of a parallelogram is equal, so we will take every angle same and their sum is equal to 360°. So, we will use angle sum property of the quadrilateral.

So -

Let the angles be 6x, 4x and 6x, 4x

Sum = 360°

Now -

We will add up, all the angles, and will put it equal to 360°. And then we will find the value of x.

On substituting the values -

$\bf \: 6x + 4x + 6x + 4x = 360 \degree \\ \\ \bf \: 20x \: = 360 \degree \\ \\ \bf \: x = \cancel \dfrac{360 \degree}{20} \\ \\ \bf \: x = 18 \degree$

$\therefore$ $\bf{x\:=\:18\degree}$

Now -

We will, put 18°, in place of x, and will multiply 6x and 4x with it, to find the measure of all the angles.

$\longrightarrow$ 6x = 6 × 18° = 108°

$\longrightarrow$ 4x = 4 × 18° = 72°

${ \therefore} \sf\: \: \: measure \: of \: all \: angles \: is \: 108 \degree \: and \: 72 \degree$

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Answer 2

$\sf Given$

Measure of two adjacent sides of Parallelogram = 6:4

$\sf To \: Find$

Angles

$\sf Solution$

Let the angles be 6x and 4x respectively

As we know that sum of all sides of a Parallelogram is 360⁰

$\bf 360 = 2(l + b)$

$\tt \implies 360 = 2(6x + 4x)$

$\tt \implies 360 = 2(10x)$

$\tt \implies 360 = 20x$

$\tt \implies x = \dfrac{360}{20}$

$\huge \frak {x = 18}$

Angles are

6x = 6(18) = 108

4x = 4(18) = 72

6x = 6(18) = 108

4x = 4(18) = 72