Question

In a quadrilateral, the angles x , (x+10), (x+20), (x+30). find the angles.​

Answer 1

Answer :-

• The angles of the quadrilateral are 75°, 85°, 95° and 105°.

Given :-

• In a quadrilateral, the angles are x, (x + 10), (x + 20) and (x + 30).

To find :-

• All the angles.

Step-by-step explanation :-

• It has been given that the angles of a quadrilateral are x, (x + 10), (x + 20) and (x + 30). We have to find the value of all the angles.

We know that :-

$\underline{\boxed{\sf Sum \: of \: all \: angles \: in \: a \: quadrilateral = 360^{\circ}.}}$

So, all these angles must add up to 360°.

$\sf \Rightarrow x + (x + 10) + (x + 20) + (x + 30) = 360^{\circ}$

Removing the brackets,

$\sf \Rightarrow x + x + 10 + x + 20 + x + 30 = 360^{\circ}$

Putting the variables and the constants separately in brackets,

$\sf\Rightarrow (x + x + x + x) + (10 + 20 + 30) = 360^{\circ}$

On simplifying,

$\sf\Rightarrow 4x + 60 = 360^{\circ}$

Transposing 60 from LHS to RHS, changing it's sign,

$\sf \Rightarrow 4x = 360^{\circ} - 60$

On simplifying,

$\sf \Rightarrow 4x = 300^{\circ}$

Transposing 4 from LHS to RHS, changing it's sign,

$\sf \Rightarrow x = \dfrac{300^{\circ}}{4}$

Dividing 300° by 4,

$\overline{\boxed{\sf \Rightarrow x = 75^{\circ}.}}$

• The value of x is 75°.

Hence, all the angles are as follows :-

$\bf x = 75^{\circ}.$

$\bf x + 10 = 75^{\circ} + 10 = 85^{\circ}.$

$\bf x + 20 = 75^{\circ} + 20 = 95^{\circ}.$

$\bf x + 30 = 75^{\circ} + 30 = 105^{\circ}.$

-----------------------------------------------------------

Note :- Kindly swipe right to see the solution clearly.

Answer 2

Answer:

We know, sum of all the angles of quadrilateral= 360°

•°• x+ (x+10)+(x+20)+(x+30)=360

=> 4x+60°=360°

=> 4x=360°-60°=300°

=> $x = \dfrac{ \cancel{300}}{ \cancel {4 \: \: } }$

=>x=75°

Correct Answer:-

• Angle 1: x=75°
• Angle 2: x+10=75+10=85°
• Angle 3: x+20=75+20=95°
• Angle 4: x+30=75+30=105°