Question

(ii) The angles of a quadrilateral are in ratio 2:5:7:10.Find the four angles
❌spammers will reported immediately❌​

Answer 1

$\: \: \: \: \: \: \:{\bold{\sf{\red{\longmapsto Question}}}}$

The angles of a quadrilateral are in ratio 2:5:7:10 .Find the four angles

$\: \: \: \: \: \: \:{\bold{\sf{\red{\longmapsto Answer}}}}$

Here , the angles of a quadrilateral are in the ratio 2 : 5 : 7 : 10 .

To find -

Find all the four angles .

Solution -

The angles of a quadrilateral are in the ratio 2 : 5 : 7 : 10 .

Let the angles be 2x , 5x, 7x and 10x respectively .

Now , as the figure is a quadrilateral, all the angles add upto 360°.

So , we can formulate the following equation -

⇛2x + 5x + 7x + 10x = 360°

⇛ 24x = 360°

⇛x = 12°

Angle A = 2x = 2 × 12° = 24°

Angle B = 5x = 5 × 12° = 60°

Angle C = 7x = 7 × 12° = 84°

Angle D = 10x = 10 × 12° = 120°

The required angles of the quadrilateral are 24°, 60° , 84° and 120° respectively .

_________________________________

Answer 2

Answer:

Question -

(ii) The angles of a quadrilateral are in ratio 2:5:7:10.Find the four angles

ㅤ

ㅤ

Given -

Angles = 2,5,710

ㅤ

ㅤ

To find -

The missing angles .

ㅤ

ㅤ

Solution-

Let's first take the given angles as = 2x,5x,7x,10x

ㅤ

Now, let's solve it further.

$2x + 5x + 7x + 10x = 360$

(reason- sum of all sides of a quadrilateral is 360°)

$7x + 7x + 10x = 360 \\ \\ = 14x + 10x = 360 \\ \\ 24x = 360 \\ \\ x = \frac{360}{24} \\ \\ x = 15$

So,

x=15°

ㅤ

ㅤ

Required Answer -

$\rightarrow$ 2x=2×x=2×15= 30°

$\rightarrow$ 5x=5×15=75°

$\rightarrow$ 7x= 7×105= 105°

$\rightarrow$ 10x= 10×15=150°