Define Corresponding Angles

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Corresponding angles are the angles that always occupy the same position at each intersection where a transverse line crosses two lines. This is shown below in figure

In this figure 1, line ‘a’ and line ‘b’ is intersected by the transversal s. And by definition, angle x and angle y are the
corresponding angles. After understanding the concepts of corresponding angles, one can easily determine the unknown angles in different situations.
This can ve clarified by the following solved examples:-          
                                                  
Example 1: Find out the angle s and t indicated in figure 2, when angle p is equal to 30 degrees.  


Solution : Given, Angle p = 30 degrees

 We know that, Angle t + Angle p = 180 degrees

 Therefore, Angle t +30 = 180 (Linear pair)

 Subtract 30 from both sides,

 Angle t + 30 – 30 = 180 – 30

 So Angle t = 150 degrees.

 Since corresponding angles are equal,

 Therefore, Angle s = 150 degrees.

Example 2: Find out the angle 1 and 1 indicated in below figure 3, when the value of angle 3 is equal to 90 degrees.

Solution : Given, The value of Angle 3 = 90 degrees

 We know that, Angle 2 + Angle 3= 180 degrees

 Therefore, Angle 2 + 90 = 180 (Linear pair)

 Subtract 90 from both sides,

 Angle 2 + 90 – 90 = 180 – 90

 So Angle 2 = 90 degrees.

 Since corresponding angles are equal,

 Therefore, Angle 1 = 90 degrees.

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