This document defines and explains different types of angles and common mistakes made in geometry regarding angles. It discusses vertical angles, complementary and supplementary angles, adjacent angles and linear pairs. It also covers angles formed by intersecting lines and transversals, including corresponding angles, alternate interior angles, and more. Finally, it defines acute, right, obtuse and straight angles based on their measurements. The overall purpose is to help students avoid common mistakes by clearly explaining angle types and definitions.

1. GEOMETRY: ANGLES
COMMON MISTAKES
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2.  Not correctly identifying the vertical
angles.
 Not realizing the angles are
congruent.
 Incorrect: Angles 1 and 2 are
congruent vertical angles.
 Correct: Angle 1 and Angle 3 are
congruent vertical angles.
Angle 2 and Angle 4 are
congruent vertical angles.
Geometry-Angles
Types and Definition of
Various Angles Common Mistakes
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 Types-Vertical,
Complementary and
Supplementary,Adjacent,
Straight
 Vertical-Definition
Vertical lines are lines
formed when two lines
intersect at a point.
 Vertical Angles are
congruent( have the same
measure),
a
b
31
2
4

3. Geometry-Angles continued
Types and Definition-
Complementary and
Supplementary
Common Mistakes
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 Complementary
Angles
are angles whose sum is
90˚.
 Supplementary Angles
are angles whose sum is
180˚.
Note: These angles do not
have to “touch”.
 Confusing which term
which goes with which
definition.
 Incorrect: Angles B and H are
supplementary angles.
 Correct: Angles B and H are
complementary angles; Angles H and
S are supplementary.
B
H
S
64˚
26˚
154˚

4. Geometry– Angles continued
Types and Definition-
Adjacent Angles and Linear
Pairs Common Mistakes
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 Adjacent Angles- angles
which share a common side or
“touch”.
 Linear Pair- adjacent angles
that are also supplementary
(their measurements add up to
180˚).
Note: Not all adjacent angles
are linear pairs; however, ALL
linear pairs are adjacent.
 Believing adjacent angles may
only be complementary or
adjacent.
 Incorrect: Angle 1 and 2 are
an adjacent linear pair.
 Correct: Angles 1 and 2 are
adjacent; Angle 3 and 4 are the
linear pair.
1 2 3 4

5. Geometry-Angles continued
Types formed by
Intersecting lines and
Transversals
Common Mistakes
 When a transversal line intersects two other
lines, parallel or not, names are given to the
angles formed based upon the position(s) in
which they lie.
 CorrespondingAngles occupy the same
position with respect to the intersecting line and
transversal (i.e. angles 1 and 5; 2 and 6; 3 and 7; 4
and 8 )
 Alternate Interior Angles lie in the interior
positions,but on opposite sides of the
transversal. (i.e. angles 4 and 6; 3 and 5)
 Alternate Exterior Angles lie in the exterior
positions,also on opposite sides of the
transversal. (i.e. angles 1 and 7; 2 and 8)
 Same-Side Interior Angles occupy the
interior positions on the same-side of the
transversal. (i.e. angles 4 and 5; 3 and 6)
 Same-Side Exterior Angles also occupy the
exterior positions but on the same-side of the
transversal. (i.e. angles 1 and 8; 2 and 7)
 Incorrectly naming the angles
formed by a transversal.
 Incorrect: Angles 2 and 6 are same-side
interior angles.
 Correct: Angles 2 an 6 are corresponding
angles.
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a
b
t
1 2
34
5 6
78

6. Geometry-Angles continued
Types defined by their Angle
Measurements Common Mistakes
 Acute Angles are angles whose
measurements are between 0˚ and
90˚ (i.e. Angle A).
 Right Angles are angles whose
measurements are 90˚ (i.e.Angle b).
 Obtuse Angles are angles whose
measurements are between 90˚ and
180˚ (i.e.Angle C).
 Straight Angles are angles
whose measurements are 180˚
(i.e. Angle D). Lines are
examples of straight angles.
 Mistaking the definitions of angles
based upon their measurements.
 Incorrect: Angle A is an obtuse angle.
 Correct: Angle A is an acute angle.
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A B C
D