ABCD is a trapezium in which `AB||DC` and `/_A=/_B=40^(@)`. Find `/_C` and `/_D`. Are these angles equal?

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the properties of the trapezium
In trapezium ABCD, we know that sides AB and DC are parallel. This means that the angles on the same side of the transversal (the non-parallel sides) are supplementary.

### Step 2: Identify the given angles
We are given that:
- Angle A = 40°
- Angle B = 40°

### Step 3: Use the property of supplementary angles
Since AB is parallel to DC, we can use the property of supplementary angles:
- Angle A + Angle D = 180°
- Angle B + Angle C = 180°

### Step 4: Calculate Angle D
Using the equation for Angle A and Angle D:
- Angle D = 180° - Angle A
- Angle D = 180° - 40°
- Angle D = 140°

### Step 5: Calculate Angle C
Using the equation for Angle B and Angle C:
- Angle C = 180° - Angle B
- Angle C = 180° - 40°
- Angle C = 140°

### Step 6: Compare Angle C and Angle D
Now we have:
- Angle C = 140°
- Angle D = 140°

### Conclusion
Both angles C and D are equal:
- Angle C = Angle D = 140°

### Final Answer
- Angle C = 140°
- Angle D = 140°
- Yes, the angles are equal.

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