Question

Find the measures of the four angles of a quadrilateral , if they are in the ratio 3:5:7:9​

Answer 1

Answer :-

• The angles are 45°, 75°, 105° and 135°.

To find :-

• The measures of the four angles of a quadrilateral.

Step-by-step explanation :-

• Here, it is given that the four angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. We have to find the measures of the angles.

Let :-

• The angles be "3x", "5x", "7x" and "9x".

We know that :-

$\underline{ \boxed{\sf Sum \: of \: all \: the \: angles_{(quadrilateral)} = 360^{\circ}}}$

Therefore,

$\longrightarrow \: 3x + 5x + 7x + 9x = 360$

$\longrightarrow \: 24x = 360$

$\longrightarrow \: x = \cancel{\dfrac{360}{24}}$

$\longrightarrow \: x = 15$

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Therefore, the angles are :-

$3x = 3 \times 15 = 45^{ \circ}$

$5x = 5 \times 15 = 75^{ \circ}$

$7x = 7 \times 15 = {105}^{ \circ}$

$9x = 9 \times 15 = {135}^{ \circ}$

Answer 2

Given that four angles of a quadrilateral are in ratio of 3:5:7:9. We have to find measures of angles.

So to solve this question, suppose that x is the common of ratio.

Therefore,

Angles of quadrilateral will be 3x,5x,7x and 9x.

__________________________

In given question, we have given angles of quadrilateral in ratio form and then we supposed that x is common of ratio and then we found angles of quadrilateral as 3x,5x,7x and 9x. Now, to solve further, we need to know some concepts to solve this problem. Quadrilateral is a plane figure made with joining four sides that means any figure that has four sides is Quadrilateral. (Parallelogram, Rectangle, square, trapezium etc are Quadrilateral.)

So here, required concept is that Sum of angles of quadrilateral is equal to 360°. This is saying that in any quadrilateral (plane figure which has 4 sides), sum of its all angles is equal to 360°.

_________________________

We concluded that, sum of angles of quadrilateral is equal to 360°

Therefore,

3x + 5x + 7x + 9x = 360°

→ 24x = 360°

→ x = 360°/24

→ x = 15°

So, from here, we concluded that common of ratio(we supposed x) is 15°

Let's put value of x in ratio:

• 3x = 3×15° = 45°
• 5x = 5×15° = 75°
• 7x = 7×15° = 105°
• 9x = 9×15° = 135°

Therefore,

Angles of quadrilateral are 45°,75°,105° and 135°