Problem Analysis:
The given image shows two intersecting lines, \( AB \) and \( CD \), with angles marked at their intersection points. The task is to determine the values of the angles \( x \) and \( y \).
Given Information:
1. The angle adjacent to \( x \) on line \( AB \) is \( 50^\circ \).
2. The angle adjacent to \( y \) on line \( CD \) is \( 130^\circ \).
Objective:
Find the values of \( x \) and \( y \).
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Step-by-Step Solution:
####
Step 1: Identify the relationship between \( x \) and the given angle.
- The angle adjacent to \( x \) on line \( AB \) is \( 50^\circ \).
- Since \( x \) and \( 50^\circ \) form a linear pair (they are supplementary angles because they lie on a straight line), their sum must be \( 180^\circ \).
\[
x + 50^\circ = 180^\circ
\]
Solving for \( x \):
\[
x = 180^\circ - 50^\circ = 130^\circ
\]
Thus, \( x = 130^\circ \).
---
####
Step 2: Identify the relationship between \( y \) and the given angle.
- The angle adjacent to \( y \) on line \( CD \) is \( 130^\circ \).
- Since \( y \) and \( 130^\circ \) form a linear pair (they are supplementary angles because they lie on a straight line), their sum must be \( 180^\circ \).
\[
y + 130^\circ = 180^\circ
\]
Solving for \( y \):
\[
y = 180^\circ - 130^\circ = 50^\circ
\]
Thus, \( y = 50^\circ \).
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Final Answer:
\[
\boxed{x = 130^\circ, y = 50^\circ}
\]
Parent Tip: Review the logic above to help your child master the concept of two parallel lines cut by a transversal worksheet.
