Question

4. The angles of a quadrilateral are (2x + 4),(2x - 1), (2x + 5)°, 2(3x + 2)°, respectively,
Find the value of x.​

Answer 1

The value of x is 29.

Given:

The angles of the quadrilateral are (2x + 4)°, (2x - 1)°, (2x + 5)° and 2(3x + 2)°.

To find:

The value of x

Solution:

According to the Angle Sum Property of the triangle, the sum of all the interior angles of a triangle is equal to 360°.

According to the given data, the four angles of the given quadrilateral are (2x + 4)°, (2x - 1)°, (2x + 5)° and 2(3x + 2)°.

Applying the Angle Sum property to the given quadrilateral,

(2x + 4)° + (2x - 1)° + (2x + 5)° + 2(3x + 2)° = 360°

=> 2x + 4 + 2x - 1 + 2x + 5 + 6x + 4 = 360

=> 12x + 12 = 360

=> x + 1 = 360 / 12

=> x = 30 - 1

=> x = 29

Hence, the value of x is 29.

#SPJ1

Answer 2

The value of x is 29

GIVEN:- (2x + 4),(2x - 1), (2x + 5)°, 2(3x + 2)°

TO FIND:- the value of x

SOLUTION:-

According to the question we are given a quadrilateral

As we know that the sum of all the angles of a quadrilateral is 360°

Thus, the sum of all the given angles = 360°

$(2x + 4) + (2x - 1) + (2x + 5) + 2 \times (3x + 2) = 360 \\ 2x + 4 + 2x - 1 + 2x + 5 + 6x + 4 = 360 \\ 12x + 12 = 360 \\ 12x = 360 - 12 \\ 12x = 348$

Dividing both sides by 12

$\frac{12x}{12} = \frac{348}{12} \\ x = 29$

Hence, the value of x is 29

#SPJ1