वह कोण ज्ञात करो जो अपने सम्पूरक का `(2)/(3)` हो।

Options

A. `40^(@)`
B. `33^(@)`
C. `72^(@)`
D. `80^(@)`

Answer

To find the angle that is \( \frac{2}{3} \) of its supplement, we can follow these steps:

### Step 1: Understand the concept of supplementary angles
Supplementary angles are two angles whose sum is \( 180^\circ \). If we denote the angle we are trying to find as \( x \), then its supplement will be \( 180^\circ - x \).

### Step 2: Set up the equation
According to the problem, the angle \( x \) is \( \frac{2}{3} \) of its supplement. We can express this relationship with the following equation:
\[ x = \frac{2}{3}(180^\circ - x) \]

### Step 3: Distribute the right side
Now, we will distribute \( \frac{2}{3} \) on the right side of the equation:
\[ x = \frac{2}{3} \times 180^\circ - \frac{2}{3}x \]
This simplifies to:
\[ x = 120^\circ - \frac{2}{3}x \]

### Step 4: Combine like terms
To combine like terms, we will add \( \frac{2}{3}x \) to both sides:
\[ x + \frac{2}{3}x = 120^\circ \]
This can be rewritten as:
\[ \frac{3}{3}x + \frac{2}{3}x = 120^\circ \]
Which simplifies to:
\[ \frac{5}{3}x = 120^\circ \]

### Step 5: Solve for \( x \)
To isolate \( x \), we multiply both sides by \( \frac{3}{5} \):
\[ x = 120^\circ \times \frac{3}{5} \]
Calculating this gives:
\[ x = \frac{360^\circ}{5} = 72^\circ \]

### Conclusion
The angle \( x \) that is \( \frac{2}{3} \) of its supplement is \( 72^\circ \).

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