The document explains the fundamentals of angles, including their definitions, classifications (acute, right, obtuse), and properties of angle pairs such as complementary and supplementary angles. It also covers concepts like congruence, the interior and exterior of angles, adjacent angles, linear pairs, and vertical angles. Overall, it provides essential geometric definitions and relationships involving angles and polygons.

1. ANGLES AND PAIRS
OF ANGLES
Math fundamentals, angle pairs,
and polygons

2. Angles and angle Measures
Definition
An angle is formed by two
noncollinear rays that have a
common endpoint. The endpoint
is the vertex of the angle, and
each ray is the side of the angle

3. Classification of angles according
Definition
An acute is an angle, which
measure is less than 90°.
A right angle is angle, which
measure is equal to 90°. It can
also be defined as an angle which
sides are perpendicular..
An obtuse angle is an angle, which

4. Congruent angles
Definition
Two angles are congruent if they
have same measure. . Means
“angle P is congruent to Angle Q”.
Similar markings are used to
indicate congruent angles.

6. Interior and Exterior of an angle.
An angle in a plane separates the
plane into three 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.

7. Interior point of an angle.
Definition
A point is in the interior of an
angle if it does not lie on the angle
itself and lies on a segment which
endpoints are on the sides of the
angle.

8. Bisector of an Angle
Definition
If D is in the interior of Then is an
angle bisector of

10. PROPERTIES OF
ANGLE PAIRS.

11. Complementary and Supplementary
angles.
TERMS ILLUSTRATIONS
Two angles are
supplementary if the sum of
their measures is 180. Each
angle is called a supplement
of the other.
If are supplementary angles,
then ma+mb=180.
Two angles are
complementary if the sum of
their measures is 90. Each
If 1 and 2 are complementary
angles, then m1 + m2=90

13. Adjacent angles
Definition
Adjacent angles are two coplanar
angles that have a common side
between them but have no
interior points in common.

15. Linear Pairs
Definition
If two angles are adjacent and
supplementary, then they are
called linear pair.

17. Vertical angles
Definition
Vertical angles are nonadjacent
angles formed by two intersecting
lines.

19. Angles at a point
Definition
All angles having the same vertex
around a point are called angles at
a point. The sum of the measures
of angles at a a point 360 degrees