Question

Angles of a quadrilateral are (4x), 5(x + 2).
(7x-20) and 6(x + 3)". Find :

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Answer 1

Question :-

The angles of a quadrilateral are (4x), 5 (x + 2), (7x - 20) and 6 (x + 3). Find the value of x and all the angles of the quadrilateral.

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Answer :-

• The value of all the angles are 64°, 90°, 92° and 114°.

• The value of x = 16°.

Given :-

• The angles of a quadrilateral are (4x), 5 (x + 2), (7x - 20) and 6 (x + 3).

To find :-

• The value of all the angles of the quadrilateral.

• The value of x.

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Step-by-step explanation :-

Detailed explanation of the solution :-

Let's understand!

We know the value of all the angles of the quadrilateral, but there are variables too. We have to isolate the variables and find the value of all the angles in constants. For that, we are going to make an equation.

Formula required :-

We know that :-

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

We will use this formula to make an equation.

Calculations :-

Using the formula given above, we can easily understand that all the angles in a quadrilateral will add up to 360°.

We know the value of all the angles (with variables), so let's start solving by making an equation.

We get :-

$\sf(4x) + 5 \: (x + 2) + (7x - 20) + 6 \: (x + 3) = 360^{\circ}$

Removing the brackets,

$\sf4x + 5x + 10 + 7x - 20 + 6x + 18 = 360^{\circ}$

Putting the constants and variables separately in brackets,

$\sf(4x + 5x + 7x + 6x) + (10 - 20 + 18) = 360^{\circ}$

On simplifying,

$\sf22x + 8 = 360^{\circ}$

Transposing 8 from LHS to RHS, changing it's sign,

$\sf22x = 360^{\circ} - 8$

On simplifying,

$\sf22x = 352^{\circ}$

Transposing 22 from LHS to RHS, changing it's sign,

$\sf x = \dfrac{352^{\circ}}{22}$

Dividing 352 by 22,

$\sf x = 16^{\circ}.$

The value of x = 16°.

We know the value of the variable (x).

So, now we can easily find the value of all the angles without variables.

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Final answer :-

We will use the value of x to find the angles.

The value of all the angles are as follows :-

4x = 4 × 16° = 64°.

5 (x + 2) = 5x + 10 = 5 × 16° + 10 = 80° + 10 = 90°.

7x - 20 = 7 × 16° - 20 = 112° - 20 = 92°.

6 (x + 3) = 6x + 18 = 6 × 16° + 18 = 96° + 18 = 114°.

Therefore, the value of the angles are 64°, 90°, 92° and 114°.

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Verification :-

To check our answer, we just have to add the values of all the angles and see whether we get 360°, since the sum of all the angles in a quadrilateral = 360°.

That way, we will also understand whether our equation was correct or not.

Let's add the values!

64° + 90° + 92° + 114° = 360°.

The sum of all the angles = 360°.

Hence verified!

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