Complementary & Supplementary Angles by Shmoop

Complementary & Supplementary Angles by Shmoop


Complementary and Supplementary Angles,
a la Shmoop. Claude the Sad Clown has been doing his best
to make kids happy at the Smiling Circus. Unfortunately, he hasn’t had much luck. A new Fun House is scheduled to be built
at the Smiling Circus, and all the clowns… …Booboo, Dimples, Twinkle-Toes, and Dr. Gigglestein… …thought it might cheer Claude up if they
allowed him to build it. Plus, that way, he won’t depress the
rest of the visitors. While building one of the windows for the
Fun House, Claude finds that the window needs a diagonal brace to support it. If the corner of the window is a right angle and the brace is at a 50 degree angle
from the bottom… …how many degrees from the side is the brace? First things first: let’s label our angles. The corner of the window is a right angle,
so let’s indicate that with a box in the corner. It’s also good to keep in mind that right
angles are 90 degrees in measure. The only other angle we know is from the bottom
to the brace, which is 50 degrees. We want to find the measure of the other angle. Since we don’t know it yet, let’s call it “X.” To solve this, we can use the
idea of complementary angles… …or two angles whose measures
add up to 90 degrees. Since “X” and the 50 degree angle add up to
90 degrees, we can find “X” by solving the equation “X plus 50 equals 90.” Subtracting 50 from both sides gives
us a value of 40 degrees for X. Feeling a little less sad, Claude goes
on to build the door. He wants to make the door to the Fun House
tilted so that it’s at an angle of 65 degrees. How tilted must the door frame be
in relation to the wall? Again, we should start by labeling our angles. We know the angle of the door is 65 degrees… …and we’ll call the other one “X” since
we don’t know it yet. Even though the doorframe is tilted, the floor
is still a straight angle. Since we know straight angles are
180 degrees in measure, the two angles here are supplementary angles… …or two angles whose measures
add up to 180 degrees. Since we know the two angles add up to 180
degrees, we can set up the equation “X” plus 65 equals 180… and solve for X. Subtracting 65 from both sides gives us “X”
equals 115 degrees… as our answer. Claude has figured out all the
angles in his Fun House, and building it has made him much happier. He still has the occasional relapse, but he’s cut down his sobbing
sessions to only about once a week.

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