Adjacent, Vertical, Supplementary, and Complementary Angles

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

These are examples of adjacent angles. 55º 35º 50º130º 80º 45º 85º 20º

These angles are NOT adjacent. 45º55º 50º 100º 35º

When 2 lines intersect, they make vertical angles (they sort form opposite V's ) 75º 105º

Vertical angles are opposite one another. 75º 105º

Vertical angles are opposite one another. 75º 105º

Vertical angles are congruent (equal). 30º150º 30º

Supplementary angles add up to 180º. 60º120º 40º 140º Adjacent and Supplementary Angles Supplementary Angles but not Adjacent

“S”upplementary add to “S”traight! Which is 180º That's how you can remember

CONGRENT SUPPLEMENTS THEOREM: One more thing about supplements, if two angles are supplementary to the same angle, the two angles are congruent! B A C So in this picture angles A and B are supplementary. And angles B and C supplementary. Sooooo – A and C are congruent (equal) (you will need to know this for your HW!!!!!!!)

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

There is also a CONGRUENT COMPLIMENTS THEOREM. Woohoo! Based on the Congruent Supplements theorem before, what do you think this one states? If two angles are complimentary to the same angle, then they are congruent!

“C”omplementary are “C”ute (another memory trick) only add up to 90º Isn't that cute! :)

One other way to remember! C comes before S in alphabet So Complimentary adds to 90º (the smaller number) And Supplementary adds to 180º (the larger number)

Before you move on, you should know these types of angles. Vertical (form opposite V, congruent) Adjacent (next to, share a common ray) Supplementary (add to 180º) Complementary (add to 90º)

Practice Time!

Directions: Identify each pair of angles as vertical, supplementary, complementary, or none of the above.

#1 Vertical, supplementary, complementary or none? 60º 120º

#1 60º 120º Supplementary Angles

#2 Vertical, supplementary, complementary or none? 60º 30º

#2 60º 30º Complementary Angles

#3 Vertical, supplementary, complementary or none? 75º

#3 75º Vertical Angles

#4 Vertical, supplementary, complementary or none ? 60º 40º

#4 60º 40º None

#5 Vertical, supplementary, complementary or none? 60º

#5 60º Vertical Angles

#6 Vertical, supplementary, complementary or none? 45º135º

#6 45º135º Supplementary Angles

# 7Vertical, supplementary, complementary or none? 65º 25º

#7 65º 25º Complementary Angles

#8 Vertical, supplementary, complementary or none? 50º 90º

#8 50º 90º None of the above

Directions: Determine the missing angle measure.

#1 45º?º?º

#1 45º135º

#2 65º ?º?º

#2 65º 25º

#3 35º ?º?º

#3 35º

#4 50º ?º?º

#4 50º 130º

#5 140º ?º?º

#5 140º

#6 40º ?º?º

#6 40º 50º