2-8 Proving Angle Relationships

You identified and used special pairs of angles.

• Use the Angle Addition Postulate to find the measure of angles.

Page 151 in your book

Protractor PostulateDoes for angles what the

Ruler Postulate does for segments. It guarantees that any angle has exactly one measure. It also ensures that all angles measures are less than 180°.

Page 151 in your book

Angle addition postulate is like the segment addition postulate. This means we can add two angles together and they will equal the one big angle.

Try It

PRNmFind

QPRmandQRPm

.132,45

M R Q

N

P

87°

Try It

.

.137

DACmandBADmFind

BACmSuppose

A

B

C

D

3X°(4X−3)°

CONSTRUCTION Using a protractor, a construction worker measures that the angle a beam makes with a ceiling is 42°. What is the measure of the angle the beam makes with the wall?

The ceiling and the wall make a 90 angle. Let 1 be the angle between the beam and the ceiling. Let 2 be the angle between the beam and the wall.

m1 + m2 = 90 Angle Addition Postulate

42 + m2 = 90 m1 = 42

42 – 42 + m2 = 90 – 42 Subtraction Property of Equality

m2 = 48 SubstitutionAnswer: The beam makes a 48° angle

with the wall.

A. 32

B. 94

C. 104

D. 116

Find m1 if m2 = 58 and mJKL = 162.

Page 152 in your book.

A. 20

B. 30

C. 40

D. 50

QUILTING The diagram shows one square for a particular quilt pattern. If mBAC = mDAE = 20, and BAE is a right angle, find mCAD.

2-8 AssignmentPage 156, 8-13

Find the measure of

each numbered angle only.