In figure, if AB ∥ CD, CD ∥ EF and y : z = 3 : 7, Find x.
126∘
Given CD || EF
⇒∠CGH=∠FHG [Alternate interior angles]
⇒∠CGH=z
Also,
∠CGI+∠CGH=180∘ [Linear pair] ⋯ (i)
∴y+z=180∘
Given: y : z = 3 : 7
Let y = 3k and z = 7k
⇒3k+7k=180∘
⇒10k=180∘
⇒k=18∘
∴z=7k=7(18)=126∘
Also, AB || CD
∴∠x=∠CGH [Corresponding angles]
⇒∠x=126∘