2. Course: Applied Geo. Aim: Complement your Supplement Aim: How to Complement your Supplement - Angle-wise Do Now: Write the definition of a linear pair on the slip of paper. Write the definition of adjacent angles. Hand the paper in with your name on it.

3. Course: Applied Geo. Aim: Complement your Supplement If the sum of the measures of two angles is 90 degrees, the angles are called complementary angles. Adjacent angles Non-adjacent angles Complementary angles may be adjacent or non-adjacent.

4. Course: Applied Geo. Aim: Complement your Supplement Sketch Pad – Complementary  s Directions: 1)Draw a right angle using the Ray Tool. 2)Make the bottom ray horizontal and the up ray by holding the Shift key. 3)Label all points with the Text Tool. 4)Measure the angle with the Measure Menu 5)Draw a 3rd ray from vertex B between the rays of the right angle. It should look similar to this 6)Measure and Label the adjacent angles formed by this new ray. 7)What must be the sum of the two angles if they are complementary?

5. Course: Applied Geo. Aim: Complement your Supplement 1 2 Find m  2, if m  1 = 73.5 0 A B C  ABC is a right angle Since  ABC is a right angle (90 0 ), the sum of  1 +  2 = 90 0. If 73.5 0 +  2 = 90 0, then  2 = 16.5 0 73.5 0 16.5 0 1 2 Find m  2, if m  1 = 48.2 0 A B C  ABC is a right angle Since  ABC is a right angle (90 0 ), the sum of  1 +  2 = 90 0. If 48.2 0 +  2 = 90 0, then  2 = 41.8 73.5 0 16.5 0

6. Course: Applied Geo. Aim: Complement your Supplement A B C  ABC is a right angle D y Find m  y, if m  x = 81.3 0 A B C  ABC is a right angle Since  ABC is a right angle (90 0 ), the sum of  x +  y = 90 0. If 81.3 0 +  y = 90 0, then  y = 8.7 0 If m  ABD = 3x + 5 and m  CBD = 28 0, find the value of x. 3x + 5 28 0 3x + 5 + 28 = 90 3x + 33 = 90 3x = 57 x = 19 x 3(19) + 5 = 62 62 + 28 = 90

7. Course: Applied Geo. Aim: Complement your Supplement Two angles are complementary. One angle measures x degrees and the other measures 2x degrees. What is the value of x and how many degrees in each of the angles? Two angles are complementary. The larger angle of the two is 14 degrees bigger than the smaller angle. How many degrees in each angle? The measure of the complement of an angle is 12 o more than twice the measure of the angle. Find the measure of the angle and its complement.

8. Course: Applied Geo. Aim: Complement your Supplement If the sum of the measures of two angles is 180 degrees, the angles are called supplementary angles. Supplementary angles may be adjacent or non-adjacent The angles show above are called a linear pair - adjacent angles that are supplementary.

9. Course: Applied Geo. Aim: Complement your Supplement Sketch Pad – Supplementary  s Directions: 1)Draw, label and measure a horizontal Straight angle with the Ray Tool. (use Shift Key) 2) Draw and label a ray from the vertex It should look similar to this 3) Measure each angle of the linear pair 4) What must be the sum of the two angles if they are supplementary?

10. Course: Applied Geo. Aim: Complement your Supplement 12  ABC is a straight angle ABC Find m  2, if m  1 = 53.7 0  1 +  2 = 180 0 If 53.7 0 +  2 = 180 0 then  2 = 126.3 0 53.7 0 126.3 0 xy  ABC is a straight angle ABC Find m  y, if m  x = 18.75 0  x +  y = 180 0 If 18.75 0 +  y = 180 0 then  y = 161.25 0 18.75 0 161.25

11. Course: Applied Geo. Aim: Complement your Supplement ABC D and m  CBD = x + 20 find the value of x and the m  CBD.  ABC is a straight angle 80x + 20 If m  ABD = 80 x + 20 + 80 = 180 x + 100 = 180 x = 80 m  CBD = x + 20 ABC D and m  CBD = 4x + 2, find the value of x and each angle.  ABC is a straight angle 2x – 84x + 2 If m  ABD = 2x – 8 m  ABD = 62 – 8 = 54 0 2x – 8 + 4x + 2 = 180 x = 31 m  ABD = 2x – 8 m  CBD = 4(31) + 2 = 126 0 m  CBD = 4x + 2 m  CBD = 80 + 20 m  CBD = 100 6x – 6 = 180 6x = 186

12. Course: Applied Geo. Aim: Complement your Supplement A B C D The larger of 2 complementary  s is twice the size of the smaller. Find the measure of each . Let x = the smaller angle Then 2x = the larger angle x + 2x = 903x = 90 x = 30 30 0 60 0 The measure of the larger of 2 supplementary  s is 15 0 more than twice the smaller. Find each . Let a = smaller  Let 2a + 15 = larger  2a + 15 + a = 180 3a + 15 = 180 3a = 165 a = 55 0 55 0 2(55 0 ) + 15 110 0 + 15 125 0 55 0 + 125 0 = 180 0 x 2x2x