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Answer 1

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$\underline{ \bf{Given - }}$

✔ The two lines are parallel.

✔Angle ABC = 105 °


$\underline{ \bf{to \: find \: - }}$

x=?


$\underline {\bf{solution \: - }}$


Angle ABC + angle CBEG= 180° (linear pair)

$\implies$105° + angle CBG =180°

$\implies$Angle CBG = 180° -105°

$\implies$Angle CBG = 75°

⟹ Now, the lines are parallel, we know that if two lines are parallel and cut by a transversal, then:-

✔ Corresponding angles are equal.

✔ Alternate angles are equal.

✔ The sum of co-interior angles is 180°


Since, angle CBG and angle DEF are corresponding angles formed on parallel lines,

so, angle DEF = 75°


$\boxed{ \bf{ \implies{x = 75}}}$

Answer 2

Answer:

$x + 105 = 180 \: (linear \: pair \: axiom)$

$x = 180 - 105$

$x = 75$

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