In figure 5.31 AB

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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