Angle and angle measures

ANGLE AND ANGLE MEASURES

ANGLE

• IT IS FORMED BY TWO NON-COLLINEAR RAYS

THAT HAVE A COMMON ENDPOINT. THE

ENDPOINT IS THE VERTEX OF THE ANGLE AND

EACH RAY IS THE SIDE OF THE ANGLE

•THE SYMBOL FOR ANGLE IS .

FOR THE ANGLE AT THE LEFT,

POINT N IS THE VERTEX AND

THE SIDES ARE 𝑁𝐴 𝑎𝑛𝑑 𝑁𝐺. THIS

ANGLE CAN ALSO BE NAMED AS

ANG, GNA,

N, OR 1.

1

A

NG

A PROTRACTOR IS USED TO MEASURE AN

ANGLE. A PROTRACTOR ASSIGNS A

NUMBER BETWEEN 0° AND 180° TO THE

ANGLE. THE NUMBER IS CALLED THE

DEGREE OF AN ANGLE. EVERY ANGLE

HAS A DEGREE MEASURE 𝑚 SUCH THAT

0° < 𝑚 <180°.

TO MEASURE AN ANGLE USING A PROTRACTOR, FOLLOW THESE STEPS,

DRAW /LAB SO THAT 𝑚/LAB = 70. USE A PROTRACTOR.

DRAW /PEN SO THAT 𝑚/PEN = 105. USE A PROTRACTOR.

PARTS OF AN ANGLE

A

NG

REFERENCE SIDE

TERMINAL SIDE

VERTEX

CLASSIFICATION OF ANGLES ACCORDING TO MEASURES

• ACUTE ANGLE IS AN ANGLE WHOSE MEASURE IS LESS THAN

90°.

• RIGHT ANGLE IS AN ANGLE WHOSE MEASURE IS EQUAL TO

90°. IT CAN ALSO BE DEFINES AS AN ANGLE WHOSE SIDES

ARE PERPENDICULAR. WE USE THE SYMBOL TO

INDICATE A RIGHT ANGLE.

• AN OBTUSE ANGLE IS AN ANGLE WHOSE MEASURE IS MORE

THAN 90°.

• A REFLEX ANGLE IS AN ANGLE WHOSE MEASURE IS GREATER

THAN 180° BUT LESS THAN 360°.

Terms Illustration If-then form

Acute angle B

A C

if / A is an acute angle, then m/ A <

90.

Right angleB

A C

If / A is a right angle, then m/ A = 90.

If / A is a right angle,

then 𝐴𝐵 𝐴𝐶

Obtuse angleB

AC

If / A is an obtuse angle, then m/ A >

90, but <180.

Reflex angle A C

B

If / A is an obtuse angle, then m/ A >

180.

Straight angle

B A

If / A is an obtuse angle, then m/ A =

180.

CONGRUENT ANGLES

EXTERIOR AND INTERIOR OF AN ANGLE

AN ANGLE IN A PLANE SEPARATES THE PLANE INTO 3 SETS OF POINTS: THE ANGLE ITSELF, THE INTERIOR OF THE ANGLE, AND THE EXTERIOR OF THE ANGLE. THE CONCEPT OF INTERIOR IS APPLIED IN THE NEXT DEFINITION.

Refer to the figure at the right. a. Name a point in the exterior of /OGE.b. Name two angles that have N as vertex. c. List all angles that have E as vertex. d. Name a pair of opposite rays.

e. List all angles that have 𝐺𝐿 as a side.f. Is /E a valid name for one of the angles in the

figure? Explain. g. Name a pair of congruent angles. h. Name angles that appear to be acute. i. Name angles that appear to be obtuse. j. Name a right angle.