Grade 8

1. ANGLE AND ANGLE
MEASURES

2. 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

3. •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
N
G

4. 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°.

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

6. DRAW /LAB SO THAT 𝑚/LAB = 70.
USE A PROTRACTOR.
DRAW /PEN SO THAT 𝑚/PEN = 105.
USE A PROTRACTOR.

7. PARTS OF AN ANGLE
A
N
G
REFERENCE
SIDE
TERMINAL
SIDE
VERTEX

8. 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

9. Terms Illustration If-then form
Acute angle B
A C
if / A is an acute
angle, then m/ A <
90.
Right angle B
A
C
If / A is a right angle,
then m/ A = 90.
If / A is a right angle,
then 𝐴𝐵 𝐴𝐶
Obtuse angle B
A
C
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 If / A is an obtuse
angle, then m/ A =

10. CONGRUENT ANGLES

12. EXTERIOR AND INTERIOR
OF AN ANGLE

13. 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.

14. 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.