Transversals

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The line which crosses two or more lines in a geometric plane is known as a transversal. If there are more number of lines crossing a set of given lines, then they all are known as transversals. When a transversal is drawn to a pair of parallel lines, then that transversal forms angles on the parallel lines which are related to every other angle on the transversal. In such cases, vertically opposite angles, corresponding angle, alternate angles etc. are formed and are equal to each other.

Example 1: In the figure shown below, the value of angle ‘a’ is 115°. If the lines AB and CD are parallel to each other and if EF is the transversal, then what is the value of ‘b’?         

Given: AB is parallel to CD.

EF is the transversal.

Value of a= 115°

If a transversal crosses a pair of parallel lines, then the alternate exterior angles are equal to each other.

Here, ‘a’ and ‘b’ are alternate exterior angles and hence a= b= 115°.

Example 2: A transversal crosses a pair of parallel lines. The angle formed by the transversal on one of the lines, x is 96°. What is the measure of its adjacent angle?

Given, a transversal crosses a pair of parallel lines.

Angle x = 96°, let its adjacent angle be = y

On a straight line, sum of two angles which are adjacent to each other = 180° (supplementary)

So x + y = 180°

96° + y = 180°

This implies: y = 180° - 96° = 84°

Therefore, its adjacent angle is 84°
 


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