Question

the angle of quadrilateral is in ratio 3:7:1:9​

Answer 1

Step-by-step explanation:

7 = 7x. 9 = 9x. Sum Of Angles Of Quadrilateral = 360°.

Answer 2

Appropriate Question:

The angles of a quadrilateral are in the ratio 3 : 7 : 1 : 9. Find the measure of each angle of a quadrilateral.

Given :

• Angles of quadrilateral are in the ratio 3 : 7 : 1 : 9.

To Find :

• We've to find the measure of each angle of a quadrilateral.

Solution :

Let all angles of a quadrilateral be 3x, 7x, 1x and 9x.

As we know,

• ${\boxed{ \bf{Sum \: of \: all \: angles_{(Quadrilateral)} = {360} \degree}}}$

Substituting values,

$\dashrightarrow \: \: \: \: \tt \: 3x + 7x + 1x + 9x = 360 \degree$

Adding up all the angles,

$\dashrightarrow \: \: \: \: \tt \: 20x = 360 \degree$

Transposing 20 to R.H.S and performing division,

$\dashrightarrow \: \: \: \: \tt \: x = \cancel \dfrac{360}{20}$

So, the value of x is,

$\dashrightarrow \: \: \: \: \tt \: \underline{ \bf{ \red{ x = 18}}} \: \:$

A.T.Q :

Now, calculating the values of all the angles in a quadrilateral,

$\implies \tt \: \: \: 3x = 3 \times 18 \\ \implies \bf \: 54 \degree$

$\implies \tt \: \: \: 7x = 7 \times 18 \\ \implies \bf \: 126 \degree$

$\implies \tt \: \: \: 1x = 1 \times 18 \\ \implies \bf \: 18 \degree$

$\implies \tt \: \: \: 9x = 9 \times 18 \\ \implies \bf \: 162 \degree$

Therefore, the measure of all angles in a quadrilateral are 54°, 126°, 18° & 162° respectively.