Question

Quadrilaterals, Class-8​

Answer 1

Question :-

• Find the value of x if x , (2x + 13°) , (3x + 10°) and (x - 6°) are all the angles of Quadrilateral?

Answer :-

• The value of x is 49°.
• The angles are 49°,111°,157° and 43°.

Given :-

• The angles of a quadrilateral are (2x + 13°) , (3x + 10°) and (x - 6°).

To find :-

The value of x and all the angles.

Step-by-step explanation :-

We know the value of all the angles of a quadrilateral with variables. We have to find the value of x by forming an equation with the given data.

We know that :-

Sum of all the angles in a quadrilateral = 360°.

We will solve the sum using this property.

So, If we add all the angles of the quadrilateral we will get 360°.

Therefore, The equation will be :-

$\sf x + (2x + 13\degree) + (3x + 10\degree) + (x - 6\degree) = 360 \degree$

Making the equation better to do the sum in more easier way,

By putting all variables a side,

$\sf (x + 2x + 3x + x) + ( 13\degree + 10\degree- 6\degree) = 360 \degree$

Adding all the variables and constants,

$\sf 7x + 17\degree = 360 \degree$

Transposing 17° from LHS to RHS, Changing its sign from (+) to (-)

$\sf 7x = 360 \degree - 17\degree$

Subtracting 17° from 360°,

$\sf 7x = 343 \degree$

Transposing 7 from LHS to RHS, Changing its sign from (×) to (÷)

$\sf x = {\dfrac{343 \degree}{7}}$

Dividing 331 by 7,

$\sf x = 49$

Thus, The value of x is equal to 49.

Therefore, The value of the angles of the quadrilateral are :-

x = 49°

2x + 13° = 2(49) + 13 = 111°

3x + 10° = 3(49) + 10 = 157°

x - 6° = 49 - 6 = 43°

Verification :-

To verify our answer, We will add all the angles of the quadrilateral and if we get 360° it's correct.

49° + 111° + 157° + 43° = 360°

360° = 360°

LHS = RHS

Hence, Verified.

Answer 2

Given:-

• The angle of a quadrilateral are (2x +13°),(3x+10°) and ( x -6°).

To Find:-

• The value of x and all the angles.

Solution:-

We know that,

$\large\sf\green{Sum\:of\:all\:angles\:in\:a\: quadrilateral=360°}$

According to the question,

x+(2x +13°) +( 3x +10°) +(x -60°) = 360°

7x + 17 °= 360°

7x = 360° - 17°

7x = 343°

x = 49°

Hence, the value of x is 49°.

Therefore,Now find the value of all angles

• x = 49°
• (2x +13°) = 2(49) +13° = 110°
• (3x + 10°) = 3(49) + 10° = 157°
• (x-6°) = 49 - 6 = 43°