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To solve the given problem, we need to determine \(\angle ADE\) based on the provided information:

### **Given Information:**
1. \(DE \parallel BC\).
2. \(\angle ABC = 118^\circ\).
3. \(\angle DAB = 42^\circ\).

### **Solution:**
#### Step 1: Understanding the geometry of the problem
Since \(DE \parallel BC\), \(\triangle ADE\) and \(\triangle ABC\) share properties related to parallel lines, particularly corresponding angles and linear angle relationships.

#### Step 2: Calculating \(\angle EAD\)
From the given information:
\[
\angle DAB = 42^\circ
\]
Thus:
\[
\angle EAD = \angle DAB = 42^\circ
\]
(These are the same because \(DE \parallel BC\) and line \(AB\) serves as the transversal.)

#### Step 3: Using linear angles to find \(\angle ADE\)
\(\angle ADE\) and \(\angle ABC\) are supplementary angles (on the same side of the transversal \(AB\)) because \(DE \parallel BC\). Therefore:
\[
\angle ADE + \angle ABC = 180^\circ
\]
Substitute \(\angle ABC = 118^\circ\):
\[
\angle ADE + 118^\circ = 180^\circ
\]
\[
\angle ADE = 180^\circ - 118^\circ = 62^\circ
\]

#### **Final Answer:**
The value of \(\angle ADE\) is **62°**.

Would you like a breakdown of the reasoning or more related problems to practice? Let me know! Here are 5 related questions to explore further:

1. If \(DE \parallel BC\), how do corresponding angles relate to each other?
2. What is the role of supplementary angles in parallel line problems?
3. Can this problem be solved using alternate interior angles?
4. If \(\angle ABC\) changes, how does \(\angle ADE\) change?
5. How would the solution differ if the lines were not parallel?

**Tip:** Always verify which angles are supplementary or corresponding when dealing with parallel lines and a transversal.

In the given figure, if DE || BC, ∠ABC = 118°, ∠DAB = 42°, then ∠ADE is equal to?

Solve a geometry problem involving parallel lines where DE || BC, ∠ABC = 118°, and ∠DAB = 42°. Learn how to calculate ∠ADE using supplementary angles and properties of parallel lines. Suitable for students in Grades 9-10.

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