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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.