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Vertical Angle Theorem, a la Shmoop.

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Mr. and Mrs. Thimbleton have just celebrated their sixty-third wedding anniversary. [Mr. and Mrs. Thimbleton in front of a big love heart]

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They're in the prime of their lives and just as in love as they were all those years ago.

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They're also just as thrill-seeking as they were back then too.

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So to celebrate, these eighty-two year old daredevils decided to go bungee jumping together.

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If they both jump in opposite directions and don't hit each other… [The Thimbleton's bungee jump off a bridge]

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…they'll make vertical angles.

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If the angle the bungee cords make at the very top is 52 degrees…

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…what angle will they make at the bottom?

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To start, let's look at Mr. Thimbleton's bungee cord. [Mr. Thimbleton hanging down from the bridge]

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Since it's a straight line, we know it makes a 180 degree angle.

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That means our top angle plus this angle on the side make a linear pair…

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…two angles that are supplementary and adjacent.

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Since they’re supplementary, we know they add up to 180 degrees.

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And because we know the top angle is 52 degrees, we can find the side angle by subtracting

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180 minus 52.

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The angle on the side is 128 degrees.

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We're looking for the measure of the very bottom angle.

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Let's consider Mrs. Thimbleton's bungee cord. [Mrs. Thimbleton hangs from the bridge]

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It also makes a 180 degree angle, which means the side angle we just found and the bottom

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angle also add up to 180 degrees.

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If we take 180 minus 128, we end up with 52 degrees as the measure of the bottom angle.

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Let's find the measure of the last angle. [Mr. Thimbleton pointing to the angle with his cane]

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If we go through the same process and pick out a supplementary linear pair…

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…we'll calculate 180 degrees minus 52 degrees equals 128 degrees.

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So really, vertical angles are any two opposite angles formed by intersecting lines.

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And the vertical angle theorem says that vertical angles are congruent… in other words, their [Mr. Thimbleton stood in front of a blackboard]

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angles are equal.

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Is this true?

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Here we have two pairs of vertical angles:

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The top and bottom, each measuring 52 degrees, and on the right and left, each measuring

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128 degrees.

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So yes.

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Vertical angles, even if they're horizontal, are congruent.

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Now you can be as secure with your knowledge of vertical angles as the Thimbletons are [The Thimbleton's jump off the bridge again and their dentures fall out]

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to their huge bungee cords.

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