1.4 –Measure and Classify Angles &Angle Constructions

Angle: Two different rays with the same initial point. Measured in degrees.

A, BAC, CAB, 1

B

A1

C

Vertex

Sides

Common initial point, where rays meet

The rays of the angle

vertex

pt. A

side

side

AB

AC

Interior Point

Exterior Point

Point inside an angle

D Pt. D is in the interior of BAC

Point outside an angle

E

Pt. E is in the exterior of BAC

Acute

Right

Obtuse

Straight

Angle more than 0°, but less than 90°

Angle more than 90°, but less than 180°

Angle that measures 90°

Angle that measures 180°

AmA = 50°

RmR = 90°

OmO = 110°

SmS = 180°

Ray that cuts an angle in half to make 2 congruent angles

QS bisects PQR

PQS SQR

Angle Bisector:

P

Q R

S

mPQS = mSQR

Note: To name an angle use “ ”, but when

stating its measure use “_______”.m

Adjacent angles: Two angles that share a common side and vertex

12

1 is adjacent to 2

Angle Addition Postulate:

If you add two adjacent angles, it totals to get their sum.

A

B

C

D

mABC + mCBD = mABD

1. Give three names for the angle shown, then name the vertex and sides.

DEF

FED

E

Vertex Sides

Pt. E ED

EF

1. Give three names for the angle shown, then name the vertex and sides.

QVS

SVQ

V

Vertex Sides

Pt. V VQ

VS

2. Classify the angle as acute, right, obtuse or straight.

mA = 115°

obtuse

2. Classify the angle as acute, right, obtuse or straight.

mA = 90°

right

2. Classify the angle as acute, right, obtuse or straight.

mA = 85°

acute

2. Classify the angle as acute, right, obtuse or straight.

mA = 180°

straight

3. Use a protractor to find the measure of the angle to the nearest degree. Then classify the angle as acute, obtuse, straight, or right.

91° obtuse

3. Use a protractor to find the measure of the angle to the nearest degree. Then classify the angle as acute, obtuse, straight, or right.

32° acute

3. Use a protractor to find the measure of the angle to the nearest degree. Then classify the angle as acute, obtuse, straight, or right.

180° straight

4. Find the indicated measure.

mPRS = 81+42

mPRS = 123°

4. Find the indicated measure.

mWXZ = 90 – 26 =

mWXZ = 64°

mNRP + mPRQ = mNRQ 8x + 7 + 4x – 1 = 78

12x + 6 = 7812x = 72

x = 6

mPRQ = 4(6) – 1

mPRQ = 24 – 1mPRQ = 23°

mADB + mBDC = mADC 11x – 7 + 5x – 3 = 118

16x – 10 = 11816x = 128

x = 8

mADB = 11(8) – 7

mADB = 88 – 7mADB = 81°

Find each indicated angle.

a = 180-160 = 20°

20°

b = 180-20 = 160°

160°

c = 180-90-75 = 15°

d = 180-90-15 = 75°

15°

Find each indicated angle.

a = 180-74 = 106°

b = 180-106 = 74°

c = 180-90-23 = 67°

d = 180-23 = 157°

74°

106°67°

157°

51°

51°mJKM =

102°mJKL =

39.5°mJKM =

79°mJKL =

39.5°

mABC =

5x + 2 = 7x – 6

2 = 2x – 6

8 = 2x4 = x

44°5(4)+2 + 7(4)-6 = 20+2 +28-6 =

5x + 13 = 9x – 23

13 = 4x – 23

36 = 4x9 = x

mABC = 116°5(9)+13 + 9(9)-23 = 45+13+81-23 =