M G 2 1 Identify angles as adjacent

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° acute 2. 90° right 3. 140° obtuse 4. 180° 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 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. 45º 15º

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

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

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

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

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

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

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

How can I remember that? • Draw the S in Supplementary S • 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 1 S 0*

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

How can I remember that? • Draw the C in Complementary C • 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… identify angles as complementary and supplementary and solve problems with Students will an unknown angle from given information about them by finding a missing angle and scoring an 80% proficiency on an exit slip.

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

3 STEPS for Finding Missing Angles: 1) First, create an addition equation by adding both angles. 1) 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 an equation. Find the value of x by making

Example 2 Find the value of x by writing your equation.

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

Example 3 Find the value of x.

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

Example 4 Find the value of x.

Example 5 Find the value of x.

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

identify angles as complementary and supplementary and solve Remember…Students will 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 1 find the missing angles you may use a protractor to draw it! T X R Q V S Z Y S