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Vertical Angle Theorem, a la Shmoop. Mr. and Mrs. Thimbleton have just celebrated
their sixty-third wedding anniversary.
They're in the prime of their lives and just as in love as they were all those years ago.
They're also just as thrill-seeking as they were back then, too, but without the parole
violations. So to celebrate, these eighty-two year old
daredevils decided to go bungee jumping together.
Let's just hope they don't lose their dentures. If they both jump in opposite directions and
don't hit each other...
...they'll make vertical angles. If the angle the bungee cords make at the
very top is 52 degrees...
...what angle will they make at the bottom? To start, let's look at Mr. Thimbleton's bungee
cord.
Since it's a straight line, we know it makes a 180 degree angle.
That means our top angle plus this angle on the side make a linear pair...
...two angles that are supplementary and adjacent.
Since they're supplementary, we know they add up to 180 degrees.
And because we know the top angle is 52 degrees, we can find the side angle by subtracting
180 minus 52.
The angle on the side is 128 degrees. We're looking for the measure of the very
bottom angle. Let's consider Mrs. Thimbleton's bungee cord.
It also makes a 180 degree angle, which means the side angle we just found and the bottom
angle also add up to 180 degrees.
If we take 180 minus 128, we end up with 52 degrees as the measure of the bottom angle.
Let's find the measure of the last angle. If we go through the same process and pick
out a supplementary linear pair...
...we'll calculate 180 degrees minus 52 degrees equals 128 degrees.
So really, vertical angles are any two opposite angles formed by intersecting lines.
And the vertical angle theorem says that vertical angles are congruent... in other words, their
angles are equal. Is this true?
Here we have two pairs of vertical angles:
The top and bottom, each measuring 52 degrees, and on the right and left, each measuring
128 degrees.
So yes. Vertical angles, even if they're horizontal, are congruent.
Now you can be as secure with your knowledge of vertical angles as the Thimbletons are
to their bungee cords.
And to their dentures too, we hope.