# 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.

Yup, Im on that wierd side of YouTube now

thank you! this really helped me!

Was actually kinda fun

this is waht happens when you wait for your dad to leave so you can play league of legends

hey guys this video sucks 🙂

what is this

kacee said sexy

thank you!!! My teacher doesn't explain anything!!!!

Thanks my teacher barely even teaches any of this stuff

but what about what if the number has another mssing part like

X=X+15?This helped somewhat but not on the supplementary angles. Disappointing

awsome

I had homework this helped me

your doodoo

you better stope

Loser haha

This helped on complementary but it kinda dose not help supplementary.

Very good

That's so easy