ABCD is a cyclic trapezium in which, `AD|\ |BC` and `angleB=70^@`. Find its remaining angles,

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the properties of a cyclic trapezium
In a cyclic trapezium, the sum of the opposite angles is equal to 180 degrees. This means:
- Angle A + Angle C = 180 degrees
- Angle B + Angle D = 180 degrees

### Step 2: Use the given information
We are given that:
- Angle B = 70 degrees

### Step 3: Find Angle D
Using the property of cyclic trapezium:
\[ \text{Angle D} + \text{Angle B} = 180^\circ \]
Substituting the value of Angle B:
\[ \text{Angle D} + 70^\circ = 180^\circ \]
Now, solve for Angle D:
\[ \text{Angle D} = 180^\circ - 70^\circ = 110^\circ \]

### Step 4: Find Angle A
Since AD is parallel to BC, we can use the property of co-interior angles:
\[ \text{Angle A} + \text{Angle B} = 180^\circ \]
Substituting the value of Angle B:
\[ \text{Angle A} + 70^\circ = 180^\circ \]
Now, solve for Angle A:
\[ \text{Angle A} = 180^\circ - 70^\circ = 110^\circ \]

### Step 5: Find Angle C
Using the property of cyclic trapezium again:
\[ \text{Angle A} + \text{Angle C} = 180^\circ \]
Substituting the value of Angle A:
\[ 110^\circ + \text{Angle C} = 180^\circ \]
Now, solve for Angle C:
\[ \text{Angle C} = 180^\circ - 110^\circ = 70^\circ \]

### Summary of Angles
- Angle A = 110 degrees
- Angle B = 70 degrees
- Angle C = 70 degrees
- Angle D = 110 degrees

### Final Answer
The remaining angles are:
- Angle A = 110 degrees
- Angle C = 70 degrees
- Angle D = 110 degrees

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