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Question
In the following figure, AB is parallel to CD; find the values of angles x, y and z:
Solution
In the given figure,
AB || CD
and LM is its transversal
∴ ∠ALM = ∠LMN (Alternate angles)
⇒ ∠x = 105°
∴ x = 105°
Similarly AB || CD and LN is its transversal
∴ ∠BLN = ∠LNM (Alternate angles)
∴ ∠z = 60°
∴ z = 60°
But x + y + z = 180° (Straight line angles)
⇒ 105° + y + 60° = 180°
⇒ y + 165° = 180°
⇒ y = 180° - 165° = 15°
Hence x = 105°, y = 15° and z = 60°
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