Question

In the adjoining figure, if x/2=y/3=z/5, then calculate the vales of x, y, z.

Answer 1

x/3 = y/4 = z/5

A,B ,C and D forms a cyclic quadrilateral.

∠ABC + ∠CDA = 180°_____1

( Also, ∠CDQ + ∠CDA = 180°________2

From (1) and (i2)
∠ABC = ∠CDQ

Also, ∠PCB = x(Vertically opp angles)

In △ CDQ, x + y + ∠CDQ = 180°
⇒ x + z + ∠ABC = 180°
⇒ x + z + (180° − ∠PBC) = 180

⇒ x + z = ∠PBC

⇒ x + z = (180° − x − y)

⇒ 2x + y + z = 180°

⇒ 2x + + = 180° 4x/3 + 5x/3

⇒ 6x+4x+5x/3 = 180° 6x+4x+5x 3

⇒ 5x = 180°
⇒ x = 36°

y = 4x/3 = 48°

z = 5x/3 = 60°