# Corresponding Angles

When two horizontal (or semi horizontal) lines are crossed by transversal line, then the angles in same relative position are known as corresponding angles

In the above figure, you can observe that:
M & N are two lines intersected by transversal line T

Following pairs are in same relative position, hence are corresponding angles

\angle 1\ and\ \angle 5
\angle 2\ and\ \angle 6
\angle 4\ and\ \angle 8
\angle 3\ and\ \angle 7

## Corresponding angles when lines are parallel

When parallel lines are intersected by transversal then the respective corresponding angles are equal.

In the above image; O & P are two parallel lines intersected by transversal T.
In this case, the corresponding angles are equal.

\angle 1\ =\ \angle 5
\angle 2\ =\ \angle 6
\angle 4\ =\ \angle 8
\angle 3\ =\ \angle 7

This is one important property to remember.
Various questions on geometry has been solved using this property.

## Corresponding Angles Property

Note the following properties:

(a) Corresponding angles lie on same side of transversal

Note \angle 1\ and\ \angle 5 are on the same left side of transversal

(b) Corresponding angles consist of one interior and one exterior angle

Interior Angle: Angles that are inside the inside the horizontal lines
\angle 3\,\ \angle 4, \angle 5,\ \angle 6 are interior angles

Exterior Angle : Angles that are outside the horizontal lines
\angle 1\,\ \angle 2, \angle 7\,\ \angle 8, are interior angles

You can see that corresponding angles \angle 2\ and\ \angle 6 involves both interior and exterior angles.

(c) Corresponding angles are equal only if the lines are parallel to each other

(d) Case of Supplementary Corresponding Angles

Two angles are supplementary when the sum of angles is 180 degree
⟹ Angle 01 + Angle 02 = 180

Corresponding angles can be supplementary when the transversal cross the parallel line perpendicularly (i.e. making 90 degree)

In the above figure, transversal crosses the parallel lines perpendicularly.

\angle 1\ = 90 degree
\angle 5\ = 90 degree

Both are corresponding angles
And, \angle 1\ + \angle 5\ = 180 degree

Hence, these corresponding angles are also supplementary angles.

## FAQ – Corresponding Angles

(01) Are all corresponding angles equal?

No!
Only if the angles are formed by parallel lines and a transversal

(02) Can corresponding angles be supplementary angles?

When two angles adds up to 180 degree, they are known as supplementary angles.

Corresponding angles can be supplementary angle when the transversal intersect the parallel lines in 90 degrees (perpendicularly)

(03) How to easily remember the corresponding angles?

Just remember two points about corresponding angles
(a) They are on same side of transversal
(b) Involves both internal and external angle

## Corresponding Angles Questions with Solutions

(01) Find the angle measurement of x

\angle A\ = 106 degree

\angle A\ and \angle x\ are corresponding angles.

Since both the lines are parallel, the corresponding angles are equal.

Hence
\angle A\ = \angle x\ = 106 degree

(02) Find the angle measurement of y

\angle A\ = 70 degree

\angle A\ and \angle y\ are corresponding angles.

Since both the lines are parallel, the corresponding angles are equal.

Hence
\angle A\ = \angle y\ = 70 degree

(03) Find angle z in the below figure

\angle A\ = 100 degree

we know that angle in straight line sums up to 180 degree
\angle A\ + \angle B\ = 180 degree
⟹ 100 + \angle B\ = 180 degree
\angle B\ = 80 degree

\angle B\ and \angle z\ are corresponding angles, hence both are equals.
\angle B\ = \angle z\

Hence,
\angle z\ = 80 degree

(04) Find angle z in the below figure

\angle A\ = \angle x\ {Corresponding Angle}
Hence, \angle x\ = 60 degree

Since QO is a straight line, the sum of angle will be 180 degree.
\angle x\ + \angle y\ = 180
⟹ 60 + \angle y\ = 180
\angle y\ = 120

We know that AB is a straight line, so sum of angles will be equal to 180 degree
\angle y\ + \angle z\ + 30 = 180
⟹ 120 + \angle z\ + 30 = 180
\angle z\ = 30

(05) Find angle b in the below figure

\angle x\ = 60 degree

then;
\angle a\ + \angle b\ = \angle x\ {Corresponding angle}
\angle a\ + \angle b\ = 60 degree – – – -eq(1)

Similarly;
\angle y\ = 130 degree

then;
\angle b\ + \angle c\ = \angle x\ {corresponding angle}
\angle b\ + \angle c\ = 130 degree – – – – eq(2)

We know that CN is a straight line.
So, all the angles in a straight line adds up to 180 degree
\angle a\ + \angle b\ + \angle c\ = 180 degree – – – – eq(3)