In the adjoining figure, AB||CD. If the `angleBAE=25^(@) and angleCDE=30^(@),` then find `angle AED`

Answer

To solve the problem step by step, we will use the properties of parallel lines and angles.

### Step 1: Identify the Given Information
We are given that:
- Lines AB and CD are parallel (AB || CD).
- Angle BAE = 25°.
- Angle CDE = 30°.

### Step 2: Draw a Construction
To find angle AED, we will draw a line PE that is parallel to AB and CD, passing through point E. This helps us to use the properties of alternate interior angles.

### Step 3: Identify Angles Using Alternate Interior Angles
Since AB is parallel to PE:
- Angle BAE (25°) is equal to angle AEP (let's call this angle 1).

Thus, we have:
- Angle AEP = 25° (by alternate interior angles).

### Step 4: Identify Another Angle Using Alternate Interior Angles
Since PE is parallel to CD:
- Angle CDE (30°) is equal to angle PED (let's call this angle 2).

Thus, we have:
- Angle PED = 30° (by alternate interior angles).

### Step 5: Calculate Angle AED
Now, angle AED can be found by adding angle AEP and angle PED:
- Angle AED = Angle AEP + Angle PED
- Angle AED = 25° + 30° = 55°.

### Final Answer
Therefore, angle AED = 55°.

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