Question

Q. The measures of angle of a quadrilateral are (n+20) , (n-20), (2n+5) (2n-5) find the value of n.​

Answer 1

Answer:

• The value of n is 60.

Clarification:

Here, we are given that measures of angle of a quadrilateral are (n+20) , (n-20), (2n+5) (2n-5) and we have to find out the value of n.

At first, we'll make a suitable equation. Thinking, which equation?! So, as we know that,

• Sum of the measure of angles of a quadrilateral is 360°.

So, this one will be the equation to get the answer. Then, by transposing terms we'll find the value of n.

Given:

• The measures of angle of a quadrilateral are (n+20) , (n-20), (2n+5) (2n-5)

To calculate:

• Value of n

Calculation:

→ Sum of the angles of a quadrilateral = 360°

Substituting values, we get :

→ (n + 20) + (n - 20) + (2n + 5) + (2n - 5) = 360°

Removing brackets,

→ n + 20 + n - 20 + 2n + 5 + 2n - 5 = 360°

Grouping all like terms,

→ n + n + 2n + 2n + 20 - 20 + 5 - 5 = 360°

Performing addition,

→ 6n + 20 - 20 + 5 - 5 = 360°

Performing substraction,

→ 6n + 0 + 0 = 360°

→ 6n = 360°

Transposing 6 from LHS to RHS.

→ $\sf { n =\cancel{ \dfrac{360}{6} } }$

Performing division,

→$\underline{\boxed{\sf{ n = 60}}} \: \red{\bigstar}$

Hence, the value of n is 60°.

Verification:

Let us verify our answer by substituting the values in the equation.

LHS :

→ Sum of the angles of a quadrilateral

→ (60 + 20)° + (60 - 20)° + [2(60) +5]° + [2(60) - 5]°

→ 80° + 40° + ( 120 + 5 )° + ( 120 - 5 )°

→ 120° + 125° + 115°

→ 360°

RHS :

→ 360°

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

LHS= RHS

Hence, verified!

Answer 2

Sum of interior angles of a quadrilateral = 360°

We are given that the angles are (n + 20), (n - 20), (2n + 5) and (2n - 5).

According to the Question:

(n + 20) + (n - 20) + (2n + 5) + (2n - 5) = 360°

⇒ n + 20 + n - 20 + 2n + 5 + 2n - 5 = 360°

⇒ 6n = 360°

⇒ n = 60°.

∴ The value of (n) here is 60°.