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Question
In the given figure, if AB || CD, then the value of x is
Options
20°
30°
45°
60°
Solution
Here AB || CD
Also, ∠1 and x are the two corresponding angles.
Then, according to the Corresponding Angles Axiom, which states:
If a transversal intersects two parallel lines, then each pair of corresponding angles are equal.
Therefore,
∠1 = x
Also, ∠1 and (120° + x) form a linear pair, therefore, their sum must be supplementary.
Therefore,
∠1 + (120° + x) = 180°
On substituting ∠1 = x in equation above, we get:
x + 120° + x = 180°
2x + 120° = 180°
2x = 180° - 120°
2x = 60°
`x = (60°)/2`
x = 30°
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