Q2 of 32 Page 60

In figure 5.31 AB || EF. Find ∠x and ∠y.

Given:


AB || EF


Construction.


Draw a line parallel to both AB and EF from the meeting point of their transverse


Theory:


If 2 lines are parallel then alternate interior angles are equal


As constructed line will divide ∠ y into 2 different parts


As the constructed line is parallel to AB


By interior alternate angles


⇒ The upper part of ∠ y = 125°


As the constructed line is parallel to EF


By interior alternate angles


⇒ The lower part of ∠ y = 141°


Combining both parts of ∠ y we get


⇒ ∠ y = 125° + 141° = 266°


As ∠ y and ∠ x make complete circle


∠ y + ∠ x = 360°


266° + ∠ x = 360°


⇒ ∠ x = 360° - 266° = 94°


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