Naming and Measuring Angles

The student will be able to (I can):

Correctly name an angle

Classify angles as acute, right, or obtuse

Use the Angle Addition Postulate to solve problems

angle

vertex

A figure formed by two rays or sides with a common endpoint.

Example:

The common endpoint of two rays or sides (plural vertices).

Example: A is the vertex of the above angle

A

C

R

Notation: An angle is named one of three different ways:

1. By the vertex and a point on each ray (vertex must be in the middle) :

TEA or AET

2. By its vertex (if only one angle): E

3. By a number: 1

Method 1 and 3 are always correct. Method 2 can only be used if there is only one angle at that vertex.

E

T

A

1

Example Which name is notnotnotnot correct for the angle below?

TRS

SRT

RST

2

R

S R

T

2

acute angle

right angle

obtuse angle

Angle whose measure is greater than 0and less than 90.

Angle whose measure is exactly 90.

Angle whose measure is greater than 90 and less than 180.

straight angle An angle whose measure is exactly 180

(also known as opposite rays, or a line)

congruent angles

Angles that have the same measure.

mWIN = mLHS

WIN LHS

Notation: Arc marks indicate congruent angles.

Notation: To write the measure of an angle, put a lowercase m in front of the angle bracket.

mWIN is read measure of angle WIN

L

HS

W

IN

interior of an angle

Angle Addition Postulate

The set of all points between the sides of an angle

If D is in the interiorinteriorinteriorinterior of ABC, then

mABD + mDBC = mABC

(part + part = whole)

Example: If mABD=50 and mABC=110, then mDBC=60

A

B

D

C

Example The mPAH = 125. Solve for x.

mPAT + mTAH = mPAH

2x + 8 + 3x + 7 = 125

5x + 15 = 125

5x = 110

x = 22

P

A

T

H

(3x+7)

(2x+8)

angle bisector A ray that divides an angle into two congruent angles.

Example:

UY bisects SUN; thus SUY YUN

or mSUY = mYUN

S

U

N

Y

Examples PUN is bisected by UT, mPUT = (3+5x)and mTUN = (3x+25). What is mPUN?

mPUT = mTUN

3 + 5x = 3x +25

2x = 22

x = 11

mPUN = 2(3 + 5(11)) = 116

P

U

N

T

Example Point R is in the interior of NFL. If mNFR = (7x 1) and mRFL = (3x+23), what value of x would make FR an angle bisector?

If FR is going to be an angle bisector, then

mNFR = mRFL

7x 1 = 3x + 23

4x = 24

x = 6

Therefore, if x = 6, then FR is an angle bisector.