Question

in the given figure angle ABD =x, angle CBD=y angle BCD=z AB is parallel to DC x=4/3y, y=3/8z find the value of x,y,z​

Answer 1

Answer:

Solution:-

Given : AB || DC ; x = 4/3y and y = 3/8z.

AB || DC,

⇒ ∠ ABD = ∠ BDC    (Alternate angles)

In Δ BDC,

x + y + z = 180°

⇒ 4/3y + 3/8z + z = 180°

⇒ First we will solve the 4/3y.

⇒ 4/3y (since he value of y = 3/8z)

⇒ 4/3 × 3/8z

⇒ 12/24z

⇒ 1/2z

Now, 1/2z + 3/8z + z = 180°

⇒ After taking L.C.M. we get,

⇒ (4z + 3z + 8z)/8 = 180°

⇒ 15z/8 = 180°

⇒ 15z = 180 × 8

⇒ z = 1440/15

⇒ z = 96°

y = 3/8z

y = (3 × 96)/8

⇒ y = 288/8

⇒ y = 36°

x= 4/3y

⇒ x = (4 × 36)/3

⇒ x = 144/3

⇒ x = 48°

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