Question

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

1.the value of x

2.each angle of quadrilateral

Answer 1

Ans.Angles of quadrilateral are (4x)°, 5(x +2)°, (7x – 20)° and 6(x +3)°.
Thus,
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°
Hence,
the value of x = 16°.
(ii) each angle of quadrilateral are
4x = 4 × 16° = 64°
5(x + 2)° = 5x + 10°
= 5 × 16° + 10° = 90°
(7x – 20)° = 7 × 16° – 20°
= 112° – 20° = 92°
and
6(x + 3)° = 6x + 18°
= 6 × 16° + 18
= 114°.