Complementary Angles and Supplementary Angles M.G. 2.1 Identify angles as adjacent, vertical, complementary and supplementary. Objective-- Students will identify angles as complementary and supplementary and solve problems with an unknown angle from given information about them by finding a missing angle and scoring an 80% proficiency on an exit slip.

Warm Up Identify the type of angle. 1. 70° 2. 90° 3. 140° 4. 180° acute right obtuse straight

Vocabulary congruent vertical angles adjacent angles complementary angles supplementary angles

Congruent angles have the same measure. Vertical angles are formed opposite each other when two lines intersect. Vertical angles have the same measure, so they are always congruent. MRP and NRQ are vertical angles. MRN and PRQ are vertical angles

Adjacent angles are side by side and have a common vertex and ray Adjacent angles are side by side and have a common vertex and ray. Adjacent angles may or may not be congruent. MRN and NRQ are adjacent angles. They share vertex R and RN. NRQ and QRP are adjacent angles. They share vertex R and RQ.

Adjacent angles are “side by side” and share a common ray. 15º 45º

These are examples of adjacent angles. 45º 80º 35º 55º 130º 50º 85º 20º

These angles are NOT adjacent. 100º 50º 35º 35º 55º 45º

When 2 lines intersect, they make vertical angles. 75º 105º 105º 75º

Vertical angles are opposite one another. 75º 105º 105º 75º

Vertical angles are opposite one another. 75º 105º 105º 75º

Vertical angles are congruent (equal). 150º 30º 150º 30º

Supplementary angles add up to 180º. 40º 120º 60º 140º Adjacent and Supplementary Angles Supplementary Angles but not Adjacent

S S S 1S0* How can I remember that? Draw the S in Supplementary Since supplementary angles equal 180*, turn that S into a number 8 by drawing a line diagonal, then add a 1 in front of that and a 0 after to make it 180. So you change the S in supplementary into 180*!! S S 1S0*

Complementary angles add up to 90º. 30º 40º 50º 60º Adjacent and Complementary Angles Complementary Angles but not Adjacent

C C C C How can I remember that? Draw the C in Complementary Since complementary angles equal 90*, turn that C into a number 9 by drawing a line, then add a 0 after that to make it 90. So you change the C in complementary into 90*!! C C C

Remember our Objective… Students will identify angles as complementary and supplementary and solve problems with an unknown angle from given information about them by finding a missing angle and scoring an 80% proficiency on an exit slip.

Supplementary Angles Remember: Two angles are supplementary if the sum of their measures is 180 degrees. Each angle is the supplement of the other. 1 2 These are supplements of each other because their angles add up to 180.

3 STEPS for Finding Missing Angles: First, create an addition equation by adding both angles. The sum of the two angles will equal 90° for Complementary Angles and 180° for Supplementary Angles. 3) Solve the equation using the inverse rules!

Example 1 Find the value of x by making an equation. This is on p. 16 of the Study Guide problem #2.

Example 2 Find the value of x by writing your equation. This is on p. 16 of the Study Guide problem #3.

Complementary Angles Two angles are complementary if the sum of their measures is 90 degrees. Each angle is the complement of the other. 1 2 These are complements of each other because their angles add up to be 90.

Example 3 Find the value of x. This is on p. 16 of the Study Guide problem #1.

1 5 2 4 3 Now, think of what we talked about today. no Are angles 4 and 5 supplementary angles? no Are angles 2 and 3 complementary angles? Are angles 4 and 3 supplementary angles? yes Are angles 2 and 1 complementary angles? yes

Example 4 Find the value of x. This is on p. 16 of the Study Guide problem #6.

Example 5 Find the value of x. This is on p. 16 of the Study Guide problem #3.

1 5 2 4 3 Think back to last class… no Are angles 1 and 2 a linear pair? no Are angles 1 and 3 adjacent angles? yes Are angles 3 and 4 a linear pair? Are angles 2 and 3 adjacent angles? yes

Let's practice. Exit Slip! Remember…Students will identify angles as complementary and supplementary and solve problems with an unknown angle from given information about them by finding a missing angle and scoring an 80% proficiency on an exit slip.

Figure 1find the missing angles you may use a protractor to draw it! X Q R V S Z Y This is the 2nd figure in the practice workbook p.16 S