If one angle of a cyclic trapezium is triple of the other, then the greater one measures

Options

A. `90^(@)`
B. `105^(@)`
C. `120^(@)`
D. `135^(@)`

Answer

To solve the problem, we need to find the measure of the greater angle in a cyclic trapezium where one angle is triple the other. Let's denote the angles as follows:

1. Let angle A = x
2. Then angle C = 3x (since one angle is triple the other)

### Step 1: Set up the equation based on the properties of the cyclic trapezium.
In a cyclic trapezium, the sum of the angles on the same side of the transversal is 180 degrees. Therefore, we have:
- Angle A + Angle C = 180 degrees

Substituting the values we have:
\[ x + 3x = 180 \]

### Step 2: Simplify the equation.
Combine the terms:
\[ 4x = 180 \]

### Step 3: Solve for x.
To find the value of x, divide both sides by 4:
\[ x = \frac{180}{4} \]
\[ x = 45 \text{ degrees} \]

### Step 4: Find the measure of the greater angle.
Now, we need to find angle C, which is 3x:
\[ \text{Angle C} = 3x = 3 \times 45 = 135 \text{ degrees} \]

### Conclusion:
The greater angle in the cyclic trapezium measures 135 degrees.