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Identifying Vertically Opposite Angles

Let’s draw a very simple pair of scissors using two straight lines. Let the lines be AB and XY. These two lines cross at O and they form four angels there. Now let’s say, for example, that one of the angles, AOY, is 110 degrees. How big are the other three angles? Knowing that both the lines are straight and straight angles equal 180 degrees, angle AOX must be 70 degrees because 110 and 70 are supplementary. Also, angle BOY must be 70 degrees for the same reason.

Do you know what the size of the fourth angle will be? If you said 110 degrees, you’re correct. You could make the size of the first angle anything you like, just as you can open scissors to any angle. And the other three angles will always follow this pattern. This makes the two opposite angles always equal. This can be shown with some simple algebra. As long as PQ and RS are straight lines, then the adjacent angles are supplementary and add to 180 degrees. So A + B equals 180. And B + C also equals 180. So A must equal C. We can use the same logic with B + C and D + C to show that B and D are equal.

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