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 smaller angle as \( x \) and the larger angle as \( 3x \).

### Step 1: Understand the properties of a cyclic trapezium
In a cyclic trapezium, the opposite angles are supplementary, which means they add up to \( 180^\circ \).

### Step 2: Set up the equation
Since one angle is \( x \) and the other angle is \( 3x \), we can write the equation based on the property of supplementary angles:
\[ x + 3x = 180^\circ \]

### Step 3: Simplify the equation
Combine like terms:
\[ 4x = 180^\circ \]

### Step 4: Solve for \( x \)
Divide both sides by 4:
\[ x = \frac{180^\circ}{4} = 45^\circ \]

### Step 5: Find the larger angle
Now, we can find the larger angle, which is \( 3x \):
\[ 3x = 3 \times 45^\circ = 135^\circ \]

### Conclusion
The greater angle in the cyclic trapezium measures \( 135^\circ \).

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