Section 1-4Angles

Angle – figure formed by 2 rays that have the same endpoint.

The rays are the _______.

The common endpoint is the _________.

When naming an angle, use __ letters, __ letter, or ___ number.

Vertex = ______Name the angle. Sides = ____ and ____

sides

vertex

3 11

point B

�⃗�𝐴 �⃗�𝐶ABC, CBA, 4, B

Name 3 angles.

ABD, DBC, ABC

Angles are measured in _________.There are 4 classifications of angles._______________ _______________Measures between Measure ____________ and _____

________________ _______________Measures between Measure _____________ and _______

degrees

acute right

straightobtuse

0° 90°90°

90° 180°180°

Protractor Postulate: Given QOP, if is paired with x and is paired with y, then mQOP = .Example 1 20° and 90°Example 2 90° and 120°Example 3 90° and 40°

= 70° = 30° = 50°

Angle Addition Postulate: If point B lies in the interior of AOC, then mAOB + mBOC = mAOC.

Angle Addition Postulate: If AOC is a straight angle, then mAOB + mBOC = 180°.

Find x, mABC, mCBD.

Angle Addition PostulatemABC + mCBD = mABD

7x + 2x = 1809x = 180

x = 20

mABC = (7x)°mABC = 7(20)mABC = 140°

mCBD = (2x)°mCBD = 2(20)mCBD = 40°

Find x and the other angle measures.

Angle Addition Postulate(3x + 4) + (2x – 4) = 90

3x + 4 + 2x – 4 = 90

x = 18

(3x + 4)°3(18) + 4

58°

(2x – 4)°2(18) – 4

32°5x = 90

congruent angles – angles that have ___________________________

adjacent angles – 2 angles in a _______ that have a _________ ________ and a _________ ______, but no common interior points

equalmeasures

planecommon vertex common side

adjacent

adjacent

nonadjacentnonadjacent

nonadjacent

bisector of an angle – a ______ that divides an angle into 2 _____________ angles

Ex. Given: bisects BED, mAEB = (19x)°, mBEC = (8x + 20)°Find x and mCED.

raycongruent

(19x)°(8x + 20)°

(8x + 20)°

(19x) + (8x + 20) + (8x + 20) = 18019x + 8x + 20 + 8x + 20 = 180

35x + 40 = 18035x = 140

x = 4

mCED = (8x + 20)°mCED = 8(4) + 20mCED = 52°

Examples:Give another name for each angle. 1. DEB 2. CBE 3. BEA 4. DAB 5. 7 6. 9

∠ 4 8 3

1 C,ECB,

ABEDCB,DCA, ECA

7. m1 + m2 = m______ 8. m3 + m4 = m______ 9. m5 + m6 = m______ or ______

EAB

AEC

EDC 180°

10. Name the vertex of 3. 11. Name the right angle.

point B

8 or BED

State another name for each angle. 12. 1 13. 6 14. EBD 15. 4

A or BAE

BDC

3

DBC

16. BDE or BDA 17. 2 18. 5 19. 9

ABE

7

C or BCD

BEA

HOMEWORK:page 21 #2-34 even