Angle and angle measures
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Transcript of Angle and angle measures
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ANGLE AND ANGLE MEASURES
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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
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•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
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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°.
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TO MEASURE AN ANGLE USING A PROTRACTOR, FOLLOW THESE STEPS,
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DRAW /LAB SO THAT 𝑚/LAB = 70. USE A PROTRACTOR.
DRAW /PEN SO THAT 𝑚/PEN = 105. USE A PROTRACTOR.
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PARTS OF AN ANGLE
A
NG
REFERENCE SIDE
TERMINAL SIDE
VERTEX
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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°.
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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.
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CONGRUENT ANGLES
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EXTERIOR AND INTERIOR OF AN ANGLE
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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.
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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.
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