Question

in a quadrilateral PQRS if angle P is 60 and angle Q,angles R and angle S is in ratio 2: 3: 7.find angles​

Answer 1

Answer:

∠P = 60°

Let x be the common multiple of ∠Q, ∠R, ∠S.

∠Q = 2x

∠R = 3x

∠S = 7x

Interior sum of the quadrilateral = 360°

⇒ ∠P + ∠Q + ∠R + ∠S = 360°

⇒ 60° + 2x + 3x + 7x = 360°

⇒ 60° + 12x = 360°

⇒ 12x = 360° - 60°

⇒ 12x = 300°

⇒ x = 300/12

⇒ x = 25°

Let's substitute the value to find ∠Q, ∠R, ∠S.

∠Q = 2x = 2(25) = 50°

∠R = 3x = 3(25) = 75°

∠S = 7x = 7(25) = 175°

Answer 2

Given :

⬤ Angle P = 60°

⬤ Angle Q , R , S is in ratio 2 : 3 : 7.

To Find :

⬤ The Angles .

Solution :

Let :

• Angle Q , R and S be 2x , 3x and 7x .

Now :

As we know that , The sum of all angles of a Quadrilateral is 360° . Hence ,

$\sf{60^{\circ}+2x+3x+7x=360^{\circ}}$

60° + 12x = 360°

12x = 360° - 60°

12x = 300°

x = 300/12

x = 25

Therefore , The Value of x is 25 .

Hence ,

Angle P = 60°

Angle Q = 2x

= 2(25)

= 50°

Angle R = 3x

= 3(25)

= 75°

Angle S = 7x

= 7(25)

= 175°

Hence , The four angles of a Quadrilateral are 60° , 50° , 75° and 175° .

Check :

60° + 2(25) + 3(25) + 7(25) = 360°

60° + 50° + 75° + 175° = 360°

360° = 360°

Hence Checked .