Same Side Exterior Angles And Their Supplementary Properties In Parallel Lines Intersected By A Transversal

Same Side Exterior Angles

Exterior angles that lie on the same side of the transversal. (3.1)

Same Side Exterior Angles are two angles that are outside the parallel lines and on the same side of the transversal. When two parallel lines are intersected by a transversal, same side exterior angles are supplementary, meaning that their sum is equal to 180 degrees.

To understand this concept better, let’s take an example:

In the given figure, we have two parallel lines (l and m) intersected by a transversal (t). A and B are two same side exterior angles.

“`
A
_________
/ \
l_____________ t ________m
\ /
B C
“`

We can see that angle A and angle B are on the same side of the transversal t and are outside the parallel lines l and m. Therefore, they are same side exterior angles.

Since l and m are parallel, angle A and angle C are corresponding angles because they are on the same side of the transversal and in corresponding positions relative to the two parallel lines. Therefore, we can write:

angle A + angle C = 180 degrees (since they form a straight line)

Similarly, angle B and angle C are also corresponding angles, and we can write:

angle B + angle C = 180 degrees

Now, if we add these two equations, we get:

angle A + angle B + 2(angle C) = 360 degrees

We know that angles A and B are same side exterior angles, and hence, they are supplementary. Therefore, we can write:

angle A + angle B = 180 degrees

Substituting this in the above equation, we get:

180 degrees + 2(angle C) = 360 degrees

Solving this equation, we get:

angle C = 90 degrees

Therefore, we can conclude that, in the given figure, the same side exterior angles A and B are supplementary, and angle C is 90 degrees.

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