SECTION 2.4

Three Types of Special Angles

1) Complementary Angles

• Complementary angles are two angles whose measures = 90o

1) Find the complement to the angle.

74om A 90o - 74o = 16o

2) Supplementary Angles

• Supplementary angles are two angles whose measures = 180o

2) Find the supplement to the angle.

74om A 180o - 74o = 106o

Challenge QuestionA supplement of an angle is three

times as large as the complement of the angle.

Find the angle.

S = 180o – A C = 90o – A

S = 3C

180o – A = 3(90o – A)

180o – A= 270o – 3A

180o + 2A= 270o

2A= 90o A= 45o

Vertical Angle Theorem:

3) Vertical Angles are

156o156o

Using Algebra to Solve for Angle Measurements

• Find the measure of all the angles.

z

x - 50

2x + 35

y + 10

x – 50 + 2x + 35 = 180o

3x – 15 = 180o

3x = 195o

x = 65o

65o - 50o 15o

= 15o y = 5

2(65) + 35 = 165o

z = 165o

PRACTICE

• Page 51 # 1 – 20 All

Vertical AnglesTHEOREM: Vertical Angles are CONGRUENT!

: 1 and 2 are vertical angles

Prove: 1 2

Given

23

1