Question

The average of 3 angles of a quadrilateral which are in the ratio of 2:5:4 is 77º. Find all
the angles of the quadrilateral.​

Answer 1

Solution :

It is given in the question that the average of three angles of a quadrilateral are in a ratio of 2 : 5 : 4 is 77 degree .

Let the angles be in the ratio of 2x, 5x and 4x respectively.

The average of these three angles is 77 degrees .

> [ 2x + 5x + 4x ]/3 = 77

> 11x/3 = 77

> x = 21

Angle 1 = 2x = 42 °

Angle 2 = 5x = 105°

Angle 3 = 4x = 84°

Let us assume that the 4th angle of the quadrilateral is a.

In a quadrilateral, the sum of all angles is 360° .

> 42° + 105° + 84° + a = 360°

> a + 231° = 360°

> a = 129°

Answer : The various angles of this quadrilateral are 42°, 105°, 84° and 129° respectively.

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Answer 2

Answer:

Given :-

• The average of 3 angles of a quadrilateral which are in the ratio of 2 : 5 : 4 is 77°.

To Find :-

• What is the all angles of a quadrilateral.

Solution :-

First, we have to find the three angles,

Let, the first angles be 2x

Second angles be 5x

And, the third angles will be 4x

According to the question,

⇒ $\sf\dfrac{2x + 5x + 4x}{3} =\: 77^{\circ}$

⇒ $\sf\dfrac{11x}{3} =\: 77^{\circ}$

⇒ $\sf 11x =\: 77^{\circ} \times 3$

⇒ $\sf 11x =\: 231^{\circ}$

⇒ $\sf x =\: \dfrac{\cancel{231^{\circ}}}{\cancel{11}}$

➠ $\sf\bold{\red{x =\: 21^{\circ}}}$

Hence, the required angles are,

✧ First angles = 2x = 2(21°) = 42°

✧ Second angles = 5x = 5(21°) = 105°

✧ Third angles = 4x = 4(21°) = 84°

∴ The three angles of a quadrilateral is 42°, 105° and 84°.

Now, we have to find the fourth angles,

Let, the fourth angles be x

As we know that,

✪ Sum of all quadrilateral = 360° ✪

According to the question by using the formula we get,

↦ $\sf 42^{\circ} + 105^{\circ} + 84^{\circ} + x =\: 360^{\circ}$

↦ $\sf 147^{\circ} + 84^{\circ} + x =\: 360^{\circ}$

↦ $\sf 231^{\circ} + x =\: 360^{\circ}$

↦ $\sf x =\: 360^{\circ} - 231^{\circ}$

➦ $\sf\bold{\purple{x =\: 129^{\circ}}}$

∴ The all angles of a quadrilateral is 42°, 105°, 84° and 129°.