# In the figure, if x/3 = y/4 = z/5 calculate x, y and z (CBSE Grade 9, 2015)

2
by va6nansimmi
which figure
Is this the image u r saying http://s10.postimg.org/f1wsadand/ck_550d390c4cc0d.jpg

• Brainly User
2016-03-20T06:35:57+05:30
Given,

= x/3 = y/4 = z/5
i, e y =  z = 4x/3 and 5x/3

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

∴ ∠ABC + ∠CDA = 180°....(1)

( Also, ∠CDQ + ∠CDA = 180°...(ii)

From (i) and (ii), ∠ABC = ∠CDQ

Also, ∠PCB = x... [Vertically opp angles Now,

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°
2016-03-20T11:42:57+05:30
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°