Question

2. In figure, if AB is parallel to CD, CD is parallel to EF and y: z = 3:7, find x.​

Answer 1

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  ^∘