Question

angles of quadrilateral so are (4x) , 5 (x+2), (7x -20) and 6(x+3). find :


- the value of x
- each angle of the quadrilateral

Answer 1

sum of all angles of a quadrilateral is 360
so
4x+5x+10 +7x-20+6x+18=360
22x=352
x=352/22
x=16


each angles are 64 ; 90 ; 92 and 114

Answer 2

The value of x = 16° and four angles of quadrilateral = 64°, 90°, 92° and 114°.

Step-by-step explanation:

We have,

The given four angles of quadrilateral=(4x)°, 5(x + 2)°, (7x - 20)° and 6(x + 3)°

To find, the value of x = ? and each angle of the quadrilateral = ?

We know that,

Sum of all angles of a quadrilateral = 360 °

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

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

⇒ 22x + 8° = 360 °

⇒ 22x = 360 ° - 8°

⇒ 22x = 352 °

⇒ $x=\dfrac{352}{22}$=16°

The value of x = 16°

Each angle of the quadrilateral,

∴ (4x)° = 4 × 16° = 64°,

5(x + 2)° = 5( 16° + 2)° = 5 × 18° = 90°,

(7x - 20)° = 7 × 16° - 20° = 112° - 20°  = 92° and

6(x + 3)° = 6( 16° + 3)° = 6 × 19° = 114°

Hence, the value of x = 16° and four angles of quadrilateral = 64°, 90°, 92° and 114°.