To solve the problem of identifying the relationship between the angles in each pair, we need to analyze the geometric properties and relationships depicted in the diagrams. Here is the step-by-step solution for each pair:
1)
-
Diagram: Two angles \( x \) and \( y \) are adjacent and form a straight line.
-
Relationship: These angles are
supplementary because they add up to \( 180^\circ \).
2)
-
Diagram: Two angles \( x \) and \( y \) are adjacent and form a straight line.
-
Relationship: These angles are
supplementary because they add up to \( 180^\circ \).
3)
-
Diagram: Two angles \( x \) and \( y \) are adjacent and share a common vertex and side.
-
Relationship: These angles are
adjacent.
4)
-
Diagram: Two angles \( x \) and \( y \) are adjacent and form a right angle.
-
Relationship: These angles are
complementary because they add up to \( 90^\circ \).
5)
-
Diagram: Two angles \( x \) and \( y \) are formed by intersecting lines and are opposite each other.
-
Relationship: These angles are
vertical angles. Vertical angles are always congruent.
6)
-
Diagram: Two angles \( x \) and \( y \) are adjacent and form a right angle.
-
Relationship: These angles are
complementary because they add up to \( 90^\circ \).
7)
-
Diagram: Two angles \( x \) and \( y \) are adjacent and form a straight line.
-
Relationship: These angles are
supplementary because they add up to \( 180^\circ \).
8)
-
Diagram: Two angles \( x \) and \( y \) are formed by intersecting lines and are opposite each other.
-
Relationship: These angles are
vertical angles. Vertical angles are always congruent.
Final Answer:
\[
\boxed{
\begin{array}{ll}
1) & \text{Supplementary} \\
2) & \text{Supplementary} \\
3) & \text{Adjacent} \\
4) & \text{Complementary} \\
5) & \text{Vertical Angles} \\
6) & \text{Complementary} \\
7) & \text{Supplementary} \\
8) & \text{Vertical Angles} \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of angle pair relationships worksheet.
