Linear Pair
A linear pair is a set of adjacent angles that form a straight line
A linear pair is a set of adjacent angles that form a straight line. In other words, when two lines intersect, the pair of angles on either side of the point of intersection add up to 180 degrees.
Let’s say we have two lines, line AB and line CD, and they intersect at point P. The angles formed by these lines are angle APB and angle CPD.
By definition, angle APB and angle CPD form a linear pair if and only if their sum is 180 degrees.
So, we can write this mathematically as:
angle APB + angle CPD = 180 degrees
For example, if angle APB measures 120 degrees, we can find the measure of angle CPD by subtracting the measure of angle APB from 180:
angle CPD = 180 degrees – angle APB
angle CPD = 180 degrees – 120 degrees
angle CPD = 60 degrees
Therefore, if angle APB measures 120 degrees, angle CPD will measure 60 degrees, and together they form a linear pair.
It is important to note that for a linear pair, the angles must be adjacent (share a common vertex and side) and they must add up to a straight angle measure of 180 degrees.
Understanding linear pairs is crucial when working on geometry problems involving parallel lines, transversals, or proving angle relationships. Linear pairs provide a basis for many angle relationships and can be used to solve various problems in geometry.
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