Angles

2. Complementary Angles
Angles are complementary if their sum adds up to 90ᵒ. (Right Angle).
65ᵒ
25ᵒ
50ᵒ
25ᵒ
65ᵒ + 25ᵒ = 90ᵒ.
The above are complementary
angles, because the sum is equal to
90ᵒ.
50ᵒ + 25ᵒ = 75ᵒ.
The above are not complementary
angles because the sum is not
equal to 90ᵒ.

3. Supplementary Angles.
Angles are supplementary if their sum adds up to 180ᵒ
135ᵒ
45ᵒ
95ᵒ
60ᵒ
45ᵒ + 135ᵒ = 180ᵒ.
The angles are
supplementary, because
the sum is equal to
180ᵒ.
60ᵒ + 95ᵒ = 155ᵒ.
The angles are not
supplementary, because
the sum is not equal to
180ᵒ.

4. Adjacent angles have a common vertex, a common side (arm) and
the other sides (arms) of the two angles lie on opposite sides of
the common side (arm).
Adjacent Angles
<A is adjacent to <B, because they
have a common vertex C and a
common side CE
1-) <ADB is adjacent to <BDC,
because they have a common
vertex D and a common side BD.
2-) <ADB is not adjacent to <ADC
because they don’t have a common
side, although they share the
same vertex D.
C
E

5. Vertically Opposite Angles
Vertically opposite angles, are pairs of opposite angles made by
intersecting lines.
They usually share the same vertex, and the sides of one line is
the extension of the other.
C
D
B
A
WZ
Y
X
OE
<AED is vertically opposite to <CEB
and <AEC is vertically opposite to
<DEB because they share the same
vertex E and the side EC is
extension of ED while side AE is
the extension of EB
In the figure above, there are no
vertically opposite angles, because
the sides of one angle are not the
extension of the other.