When two lines or more than two parallel lines are cut across by a transverse line, then angles created are known to be an alternate exterior angles. These specific Exterior angles are set on the outer portions of the Transversal line, on the varied sides.
What Are Linear Pairs of Angles?
When the two lines come together and cut across each other, the angles formed are recognized to be linear pairs of angles. These linear pairs of angles are neighbouring to each other. The total of the linear pairs of angles is 180 degrees. Those angles whose total amount is 180 degrees are identified as supplementary angles.
How To Find Alternate Exterior Angles?
To find the Alternate pairs of Exterior angles, here are the steps to find out.
- Step 1: First of all, find all the angles that lie on the exterior portions of the parallel lines cut crossed.
- Step 2: Then in the next step, find the alternate pairs of the alternate exterior angles.
- Step 3: Those pairs of alternate exterior angles will be similar to each other.
Some Examples of Alternate Exterior Angles
Here, we will be mentioning some of the examples to give better concepts and grasping of the particular topic.
- If there are two parallel lines, AB and XY. These two parallel lines are cut across by a transversal line TU. The angles formed are named, 1,2,3,4,5,6, 7and 8. The alternate exterior angles in all these eight angles will be the angles that are formed on the external of that space made by the transversal and parallel line. Let’s suppose that those exterior angles are 1,2,7 and 8. Then, the angles of 1 and angle 8 will lie on the alternate sides, externally. Then these angles will be identical to each other.
- Now taking another example, If there are another two parallel lines named, HI and OP. Both of the parallel lines are cut across by a transversal line named, VB. The result of this will be the eight angles formation. The names of these angles are, A, T, X, V, U, L, M, and D. Let’s suppose that A, T, M, and D lie on the external portions of the space formed by the result of cutting of the parallel lines, HI and OP by the transversal line, VB. Then, the angles, angle A, and angle D will be similar to each other.
Some Examples Of Linear Pair Of Angles
Here, we will be mentioning a few examples of linear pairs of angles through which one will get a better understanding of this specific topic.
- Let us suppose that there is a line segment named, XY. A ray, named OZ, is put across this particular line segment, XY. Then, there is a formation of two angles, due to this circumstance made up by that ray and that line segment. Those two angles formed are named angle ZOX and the other angle is the angle ZOY. Both angles are composed of a set of linear pairs of angles. The angle that is formed between the OX and OY is 180 degrees. Thus, the sum of the linear pairs of angles is 180 degrees.
- Let’s take another example. There is a line segment named, PY. There is a ray, named LK, that is standing on this line PY. Then the angles formed by these will be, angle KLP and the other angle will be angle KLY. Both angles will be linear pairs of angles.
What Is Alternate Angle Theorem?
According to this Alternate Angle Theorem, it is declared that when two or more two parallel lines will be cut across by the Transversal line, then the Alternate angles formed will be identical to each other.
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