Complementary and Supplementary Angles

Today’s Learning Goals We will develop the idea that complementary angles are two (or more) angles that add up to 90 . We will develop the idea that supplementary angles are two (or more) angles that add up to 180 . We will determine the complement and supplement of given angles. We will think about when complementary and supplementary angles are useful in our world.

Review of Angle Terms What is an acute angle? Yes…any angle that is less than 90 . What is a right angle? Great…any angle that is exactly 90 . What is an obtuse angle? Great…any angle that is more than 90 .

Right Angles Right angles (90  angles) are very important to us. What inside this classroom has a right angle? Excellent…the door frame, the ceiling tiles, the window frame, the walls, etc. What in this picture of a football field has a right angle? Nice…the corners, the field goal posts, the lines in the middle of the field, etc.

Angles put together Many things that we use every day depends on the use of right angles. Sometimes, it is necessary to piece together two smaller items to create the right angles. Artists, interior designers, and architects often piece together smaller items to create right angles in their work. Where are the right angles in the following Tibetan artwork? Do you see how the right angles are made of smaller angles put together?

Quilting and Right Angles Quilting is another type of artwork or craft that uses different shapes of fabric put together. Often times, squares are the main shape. Other shapes can be put together to form a square. What shapes were put together to form the pinwheel quilting square below? Then, the squares are put together to form the quilt. Nice…8 identical triangles were put together to form a square.

Quilting and Right Angles For the pinwheel quilting square below, what did the highlighted angle measurement have to be so that two of them would make a right angled corner? Great…45  because 45  + 45  = 90 . Complementary angles are angles that add up to exactly 90 . So, 45  and 45  are complementary!

10  Quilting and Angles Tanya’s grandmother makes quilts. She uses scraps of old material to make squares. Below are some pieces of scraps that Tanya’s grandmother has in her house. 40  Can Tanya’s grandmother put together the two blue triangles to form a square (without flipping the material over)? No…because 40  + 40   90  !

10  Quilting and Angles Suppose we slide the two blue triangles together. What angle measure is needed to make a right angle in the top left-hand corner? 40  The three angles 40 , 10 , and 40  are also complementary because they add up to 90  exactly. 40  Yes…10 .

Complementary Angles Consider the following right angles. Find the missing complementary angle for each. a) 20  ? Yes…m(?) = 70 . b) 23  12  ? Good…m(?) = 55 .

Quilting and Angles Tanya’s grandmother decided to make a quilt using the pinwheel design and some of the scraps that she had laying around the house. She came up with the following design for a square that is made from nine smaller squares. Notice that the four highlighted squares are the squares made from the two triangles and the kite shape we discussed previously.

Quilting and Supplementary Angles The edges of the quilt are straight. Consider the highlighted edge of the quilt. What are the two angle measurements highlighted below that add up to a straight line (180  )? Yes…90  because 90  + 90  = 180 . Supplementary angles are angles that add up to exactly 180 . So, 90  and 90  are supplementary!

Quilting and Supplementary Angles There are other supplementary angles in the large square below. Consider the following highlighted smaller square enlarged to the right. 60 

Quilting and Supplementary Angles Consider the highlighted edge of this square. This edge is also straight. 60  ? What would the measurement of the highlighted angle have to be if the other two are 60  ? Excellent…60  because 60  + 60  + 60  = 180  The three angles 60 , 60 , and 60  are also supplementary because they add up to 180  exactly.

Quilting and Supplementary Angles Now consider the highlighted edge of the same square. This edge is also straight. 30  ? What would the measurement of the highlighted angle have to be if the other one is 30  ? Excellent…150  because 30   = 180  The two angles 30  and 150  are also supplementary because they add up to 180  exactly.

Partner Work You have 15 minutes to work on the following problems with your partner.

For those that finish early Find the complement of the following angles: a) 43 , ? , 22  b) 18 , 54 , ?  c) ? , 36  Find the supplement of the following angles: a) 24 , 19 , ? b) 108 , ? , 43 , 16  c) 77 , ? 

Big Idea from Today’s Lesson Complementary angles are angles that add up to exactly 90 . Supplementary angles are angles that add up to exactly 180 . It is possible to use more than two angles to make a 90  angle or a 180  angle.

Homework Pgs. 215 – 216 (2 – 20) You need a protractor to answer some of the problems.