Angle Relationships # 1a
Angle Relationships
Definitions:
Opposite Angles:
the equal angles formed by 2 intersecting lines. The angles are
across from each other.
Eg.
A
Supplementary Angles:
A=C
B=D
B
D
C
two or more angles whose sum is 180 degrees.
Eg.
A
B
x
A + B = 180°
y
z
x + y + z = 180°
Complementary Angles: two or more angles whose sum is 90 degrees.
Eg.
b
a
a + b = 90°
Rules for Finding the Relationship Between Angles
1.
Whenever two straight lines cross, all four angles are related to one another.
2.
The angles across from each other are the same (opposite angles).
3.
The angles along the same line add up to 180 degrees (supplementary angles).
4.
5.
The angles that make up a right angle add up to 90 degrees (complementary angles).
When expressing your answer: state the angle (letter), the value of the angle, the
rule for finding the angle and the angle you compared the rule too.
6.
Whenever possible, use a rule that compares an unknown angle with an angle that is
given.
Examples:
1.
Find the missing angles and state the rule for finding the angle compared to the angle
given.
D
70°
w
A
x
B
z
y
C
E
w = 110°
x = 70°
y = 20°
supplementary angle to 70°
opposite angle to 70°
complementary angle to x
y + z =w
20° + 90° = 110°
opposite angles
2.
Write the complementary angle to 20°
90° - 20°
= 70°
3.
Write the supplementary angle to 140°
180° - 140°
= 40°