Question

AB ll CD CD Parallel EF and y ratio z find X plz tell ​

Answer 1

$\Large\mathtt\green{ }\huge\underline\mathtt\red{Answer : }$

In the given figure,AB∥CD,CD\parallel EFandy:z=3:7$$

Let y=3a and z=7a

∠DHI=y(vertically opposite angles)

∠DHI+∠FIH=180∘ (Interior angles on the same side of the transversal) 

⇒y+z=180∘

⇒3a+7a=180∘

⇒10a=180∘ or a=18∘

∴y=3×18∘=54∘ and z=7×18∘=126∘

Also,x+y=180∘

⇒x+54∘=180∘

∴x=180∘−54∘=126∘

Hence,x=126

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Answer 2

$\huge\bold\green{Solution}$

$\huge\boxed{\fcolorbox{purple}{ink}{GIVEN:}}$

$AB \: || \: CD \: and \: CD \: || \: EF$

• ∴ AB || CD || EF (Lines parallel to the same line are parallel to each other)

• As AB//CD and CD //EF
• Therefore, AB//CD//EF

• x = z 
• (Alternate interior angles) (1)

Angle X= angle Z (alternate interior angles are equal.

• It is given that y: z = 3: 7

• Ratio of angle Y : angle Z = 3 : 7

• Let the common ratio between y and z be a.

$∴ y = 3a and z = 7a$

• Also, x + y = 180º (Co-interior angles on the same side of the transversal)

• z + y = 180°   [Using equation (1)]

$7a + 3a = 180º \\10a = 180º \\a = 18º \\∴ x = 7a = 7 × 18º = 126º$