Question

The angles of a quadrilateral are
5x0, 5(x+2)0, (6x-20)0 and 6 (x+3)0 respectively. Find the measure of each angle.

Answer 1

Answer :-

• The measure of all the angles are 80°, 90°, 76° and 114°.

Step-by-step explanation :-

To Find :-

• The measure of all angles of a quadrilateral

Solution :-

Given that,

• The angles of a quadrilateral are
• 5x°, 5(x+2)°, (6x-20)° and 6(x+3)° respectively

As we know that,

Sum of all angles of quadrilateral = 360°, Therefore,

• 5x + 5(x+2) + (6x-20) + 6(x+3) = 360°

=> 5x + 5(x+2) + (6x-20) + 6(x+3) = 360

=> 5x + 5x + 10 + 6x - 20 + 6x + 18 = 360

=> 5x + 5x + 6x + 6x = 360 - 10 + 20 - 18

=> 10x + 12x = 350 + 20 - 18

=> 22x = 350 + 2

=> 22x = 352

=> x = 352/22

=> x = 16

• The value of x is 16.

Now, the angles are :-

• 5x

=> 5*16

=> 80°

• 5(x+2)

=> 5(16+2)

=> 5*18

=> 90°

• (6x-20)

=> (6*16-20)

=> (96-20)

=> 76°

• 6(x+3)

=> 6(16+3)

=> 6*19

=> 114°

Hence, The measure of all the angles are 80°, 90°, 76° and 114°.

Answer 2

Angles of quadrilateral are,

(4x)°, 5(x + 2)°, (7x - 20)° and 6(x + 3)°.

4x + 5(x + 2) + (7x - 20) + 6(x + 3) = 360°

4x + 5x + 10 + 7x - 20 + 6x + 18 = 360° = 22x + 8 = 360°

22x = 360°- 8°

22x = 352°

x = 16°

Hence angles are,

(4x)° = (4 × 16)° = 64°,

5(x + 2)° = 5 (16 + 2)° = 90°,

(7x - 20)° = (7 × 16 - 20)° = 92°

6(x + 3)° = 6(16 + 3) = 114°