ShmoopTube

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Complementary and supplementary angles a la shmoop

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Claude the sad clown has been doing his best to make kids happy at the smiling [Claud riding a small bicycle]

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circus unfortunately he hasn't had much luck a

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new funhouse is scheduled to be built at the smiling circus and all the clowns

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boo boo, dimples, twinkle toes and dr. gigglestein, but it might cheer Claude

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if they allowed him to build it...Plus that way he won't depress the rest of [little girl crying]

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the visitors while building one of the windows for the funhouse

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Claude finds that the window needs a diagonal brace to support it if the

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corner of the window is at a right angle and the brace is at a 50 degree angle

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from the bottom how many degrees from the side is the brace? all right so let's [Girl sitting at a table with a coffee]

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think this through first things first let's label our angles the corner of the

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window is a right angle so let's indicate that with a box in the corner

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it's also good to keep in mind that right angles are 90 degrees in measure

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the only other angle we know is from the bottom to the brace which is 50 degrees

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we want to find the measure of the other angle since we don't know it yet let's

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call it X to solve this we can use the idea of complementary angles or two [Two angles complementing each other]

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angles whose measures add up to 90 degrees since X and the 50 degree angle

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add up to 90 degrees we can find X by solving the equation X plus 50 equals 90

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subtracting 50 from both sides gives us a value of 40 degrees for X feeling a

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little less sad Claude goes on to build the floor he wants to make the door to [Claude appears with a hammer]

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the funhouse tilted so that it's at an angle of 65 degrees

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how tilted must the doorframe be in relation to the wall? Again we should

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start by labeling our angles we know that the angle of the door is 65 degrees

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and we'll call the other one X since we don't know it yet even though the door

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frame is tilted the floor is still a straight angle since we know straight [Tilted door appears]

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angles are 180 degrees in measure the two angles here are supplementary

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angles or two angles whose measures add up to 180 degrees... since we know that two

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angles add up to 180 degrees we can set the equation X plus 65 equals 180 and

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solve for X so subtracting 65 from both sides gives us x equals 115 degrees as [65 subtracted from both angles]

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our answer Claude has figured out all the angles in

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his funhouse and building it has made him much happier he still has the

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occasional relapse but he's cut down his sobbing sessions to only about once [Claude sobbing and the Joker appears]

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a week

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