Qstnid -C-3- Angles Of A Quadrilateral Are (4x)°, 5(x + 2)°, (7x - 20)° And 6(x + 3)°. Find : (I) The Value Of X. (Ii) Each Angle Of The Quadrilateral. - 16: Understanding Shapes (Including Polygons) Class 8 Maths - Icse-viii-mathematics

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ICSE-VIII-Mathematics

16: Understanding Shapes (Including Polygons) Class 8 Maths

with Solutions - page 4

Qstn# C-3 Prvs-Qstn Next-Qstn

#3
Angles of a quadrilateral are (4x)°, 5(x + 2)°, (7x - 20)° and 6(x + 3)°. Find : (i) the value of x. (ii) each angle of the quadrilateral.
Ans : 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 angle 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˚