In the figures given below AB || CD. EF is the transversal intersecting AB and CD at G and H respectively. Find the values of x and y. Give reasons

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Solution

$∠ C G H + ∠ C G E = 180^{\circ}$ (Supplementary angles)
$y + 2 x = 180^{\circ} . . . . . (i)$
$∠ C G H = ∠ G H B$ (Alternate angles)
$y = 3 x . . . . . . (i i)$
Solving $(i)$ and $(i i)$
$\Rightarrow x = 36^{\circ} y = 3 x = 3 \times 36^{\circ} = 108^{\circ}$

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In the figures given below AB || CD. EF is the transversal intersecting AB and CD at G and H respectively. Find the values of x and y. Give reasons

∠CGH+∠CGE=180∘ (Supplementary angles)y+2x=180∘.....(i)∠CGH=∠GHB (Alternate angles)y=3x......(ii)Solving (i) and (ii)⇒x=36∘y=3x=3×36∘=108∘

$∠ C G H + ∠ C G E = 180^{\circ}$ (Supplementary angles)
$y + 2 x = 180^{\circ} . . . . . (i)$
$∠ C G H = ∠ G H B$ (Alternate angles)
$y = 3 x . . . . . . (i i)$
Solving $(i)$ and $(i i)$
$\Rightarrow x = 36^{\circ} y = 3 x = 3 \times 36^{\circ} = 108^{\circ}$