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2. In Fig. 6.29, if AB || CD, CD || EF and y: Z=3:7, find x. fig. 6.29​

Answer»

QUESTION

\sf \: In \: Fig. 6.29, if \: AB || CD, CD || EF \: and \: y : z = 3 : 7, find \: x.

SOLUTION:

\sf \: Given, y : z = 3 : 7 \\ \sf \: Let ∠ y = 3a\\ \sf \:Then ∠z = 7b\\ \sf \:∠x \: and \: ∠z \: are \: alternate \: interior \: angles \: of \: parallel \: lines \: so \: that\\ \sf \:∠x = ∠z \: \: \: \: \: \: \: \: \: \: \: →①\\ \sf \:Sum \: of \: interior \: angle \: on \: the \: same \: side = 180°\\ \sf \:x + y = 180°\\ \sf \:putting \: value \: of \: x \: from \: equation ①\\ \sf \:z + y = 180°\\ \sf \:putting \: the \: value \: of \: z \: and \: y \\ \sf \:7a + 3a = 180°\\ \sf \:10 a = 180°a = \frac{180}{10} \\ \sf \:a = 18 \\ \\ \sf \:y = 3a \: \: \: = 3x18 \: \: \: \: \: = 54°\\ \sf \:z = 7a \: \: \: = 7x18 \: \: \: \: \: \: = 126°\\ \sf \:x = z = 126°

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