Adjacent, Vertical, Supplementary, and Complementary Angles

Adjacent angles 45º 15º Angles that are “side by side” and share a common ray are called?

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

These angles are examples of? 45º55º 50º 100º 35º Non- Adjacent

When 2 lines intersect, they make what type of angles? 75º 105º vertical angles

What type of angles are opposite one another? 75º 105º Vertical angles

Vertical angles are opposite one another. What is the measure of angle A? 75º A 105º

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

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

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

Angles Around a Point Angles around a point will always add up to The angles above all add to 360° 53° + 80° + 140° + 87° = 360° 360 degrees.

Practice Time!

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

#1 60º 120º

#1 60º 120º Supplementary Angles

#2 60º 30º

#2 60º 30º Complementary Angles

#3 75º

#3 75º Vertical Angles

#4 60º 40º

#4 60º 40º None of the above

#5 60º

#5 60º Vertical Angles

#6 45º135º

#6 45º135º Supplementary Angles

#7 65º 25º

#7 65º 25º Complementary Angles

#8 50º 90º

#8 50º 90º None of the above

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

Name the adjacent angles and linear pair of angles in the given figure: Adjacent angles:  ABD and  DBC  ABE and  DBA Linear pair of angles:  EBA,  ABC C D B A E  EBD,  DBC C D B A E

Name the vertically opposite angles and adjacent angles in the given figure: A D B C P Vertically opposite angles:  APC and  BPD  APB and  CPD Adjacent angles:  APC and  CPD  APB and  BPD

Pairs Of Angles Formed by a Transversal Corresponding angles Alternate angles Interior angles

Corresponding Angles When two parallel lines are cut by a transversal, pairs of corresponding angles are formed. Four pairs of corresponding angles are formed. Corresponding pairs of angles are congruent.  GPB =  PQE  GPA =  PQD  BPQ =  EQF  APQ =  DQF Line M B A Line N D E L P Q G F Line L

Alternate Angles Alternate angles are formed on opposite sides of the transversal and at different intersecting points. Line M B A Line N D E L P Q G F Line L  BPQ =  DQP  APQ =  EQP Pairs of alternate angles are congruent. Two pairs of alternate angles are formed.

The angles that lie in the area between the two parallel lines that are cut by a transversal, are called interior angles. A pair of interior angles lie on the same side of the transversal. The measures of interior angles in each pair add up to Interior Angles Line M B A Line N D E L P Q G F Line L  BPQ +  EQP =  APQ +  DQP = 180 0

Name the pairs of the following angles formed by a transversal. Line M B A Line N DE P Q G F Line L Line M B A Line N D E P Q G F Line L Line M B A Line N D E P Q G F Line L

Directions: Determine the missing angle.

#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

Find the value of x.

#5 140º ?º?º

#5 140º

Find the value of x.

#6 40º ?º?º

#6 40º 50º