ANGLES

1. A N G L E S

2. A n g l e s
It is figured formed by two rays
with a common endpoint, and
which are not on the same line.
The two rays are the sides of the
angle and the common endpoint
is called the vertex.

3. A n g l e s
An angle is named using a number, vertex
or a vertex and points on each side.
• If three letters are used to name an
angle, the middle letter should be the
vertex.
• If one letter is used, it should be the
vertex.

4. A n g l e s
Angles are measured using a
protractor and the unit of
measurement is degrees (°).

5. A n g l e s
Types of Angles

6. ACUTE ANGLE
OBTUSE ANGLE
RIGHT ANGLE
STRAIGHT ANGLE

7. A c u t e A n g l e s
An acute angle is an angle
whose measure is greater than
0° but less than 90°.

8. R i g h t A n g l e s
A right angle is an angle whose
measure is exactly 90°. If an angle is a
right angle, then the sides are
perpendicular to one another

9. O b t u s e A n g l e s
An obtuse angle is an angle
whose measure is greater than
90° but less than 180°.

10. Relationships Between Angles
Adjacent angles are two distinct
angles with common vertex and a
common side.

11. Complementary Angles
Supplementary Angles

12. C o m p l e m e n t a r y A n g l e s
- are two angles whose sum of measure
equals 90°

13. S u p p l e m e n t a r y A n g l e s
- are two angles whose
measures have the sum of
180°

14. E x a m p l e 1
Two angles are adjacent if they have
common vertex and a common side.
In the figure, are adjacent angles
since their vertex is at point 0 and
their common side is ray.

16. E x a m p l e 2
What must be the measure of
K to complement J?
72°
J
K
Solution: Sum of
complementary angles
is 90°.
J = 72° ; K = x°
J + K = 90°
72° + x° = 90°
x = 90° - 72°
x = 18°
Checking: 72° + 18° = 90°
Answer: Angle K measures 18°

17. E x a m p l e 2
Two angles, 1 and 2 are
supplementary. If 2 measures 86°,
what is the measure of 1?
Solution: Sum of supplementary
angles is 180°.
1 + 2 = 180°
x + 86° = 180°
x = 180° - 86°
x = 94°
Checking: 94° +86° = 180°
Answer: 1 measures 94°

18. L i n e a r P a i r
It is composed of two
adjacent angles whose
measures have the sum
of 180°. These are
adjacent angles that
formed a straight line.

19. V e r t i c a l A n g l e s
- are two nonadjacent angles
formed by two intersecting
lines. Vertical angles are
congruent.

20. Q u i c k S e a t w o r k
What are the values of the
variables?
z
y
x
46°

21. Parallel Cut by a Transversal
Given 𝑙1is parallel to 𝑙2 and 𝑙3
is a transversal line.
𝑙2
𝑙1
𝑙3
e
f g
h
b
a
c
d

22. Parallel Cut by a Transversal
Given that the parallel lines are cut
by a transversal, the following
relationships are true:
1. Alternate interior angles are
congruent.
2. Alternate exterior angles are
congruent.