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Answer :

It is given that, y : z = 3:7

Let, y = 3k and z = 7k,

x = \(\angle{CHG}\) (Corresponding angles) ....(i)

Z = \(\angle{CHG}\) (Alternate angles) ....(ii)

From (i) and (ii), we get,

\(\therefore \) x = z ....(iii)

Now, x + y = \(180^\circ\) ....(Internal angles on the same side of the transversal)

From eq.(iii),

z + y = \(180^\circ\)

\(\Rightarrow \) 3k + 7k = \(180^\circ\)

\(\Rightarrow \) 10k = \(180^\circ\)

\(\Rightarrow \) k = \(18^\circ\)

\(\therefore \) y = 3 × \(18^\circ\) and z = 7 × \(18^\circ\)

\(\therefore \) y = \(54^\circ\) and z = \(126^\circ\)

Hence, x = \(126^\circ\)

- In figure, find the values of x and y and then show that AB ||CD.
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