What Are Corresponding Angle

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					           What Are Corresponding Angle
What Are Corresponding Angle

In mathematical geometry, when a transversal passes through the two parallel
lines at different points then it forms a corresponding angles. In a simple mean we
can say that when two parallel lines are intersected by the third line then the
newly generated angles in matching corners are known as corresponding angles.

 Suppose there is a line L which act as a transversal for two parallel lines ‘a’ and
‘b’ then eight angles are formed there. These eight angles are categorized into
two categories.

First category is known as interior angles and second category are known as
exterior angles. Interior angles are those which are defined between the line of a
and b. In the same aspect remaining angles are known as exterior angles.

Through the above definition we can say that corresponding angles are two
congruent angles which are lies on the same side of the transversal line ‘L’ and
they are situated the same way on two different parallel lines. In the below we
show you a diagram which helps in understanding the Corresponding Angles
Definition.
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In the above diagram we can see that there are two parallel lines ‘a’ and ‘b’ which
are intersected by the third line L. Due to the intersection of line a and b by the
line L there are eight angles formed which named as angle p, angle q, angle r,
angle s, angle u, angle v, angle w and angle x. In the above the angle r, angle s,
angle u and angle v are known as interior angles because they are formed
between the line ‘a’ and line ‘b’. In the same aspect angle p, angle q, angle w and
angle x are known as exterior angles. Due to this there are four corresponding
angles formed which are given below:

∠q is equal to the ∠v,

And ∠p is equal to ∠u,

And ∠r is equal to ∠w,

And ∠s is equal to ∠s

Now we show you how corresponding angles are helpful in calculating the
measurement of an angle.

Example a: suppose there is a figure as like shown above, if there is an angle ‘q’
which has the measure of 45 degree. Now we need to find the measure of other
seven angles by following the property of corresponding angles?

Solution: In the above question given that angle ‘q’ is equal to the 44 degree

then ∠v= 45 degree because according to corresponding angle definition ∠v and
∠q are the corresponding angles. So, the angles ‘∠v’ and ‘∠q’ are equal to each
other. Therefore ∠v = 45 degree.


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As we all are very well aware that a straight angle has the measure of 180 degree.

So, ∠q+ ∠p = 180 degree.

45 degree + ∠p = 180,

∠p = 180 – 45,

∠p = 135 degree,

 Here ∠r and ∠u are corresponding angles. Therefore, ∠r and ∠u are equal.
Therefore, ∠u is also 138 degree.

We know that, a straight angle has a measure of 180 degree. So, ∠p +∠q= 180
degree.

42 + ∠q= 180,

∠q = 180 – 42,

∠q = 138,

According to the corresponding angle definition ∠p and ∠u are corresponding
angles. Then, ∠p and ∠u are equal to each other. Therefore, ∠u is also 138
degree.




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posted:7/13/2012
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