If two supplementary angles differ by `36^@` , find the angles.

Answer

To find the two supplementary angles that differ by \(36^\circ\), we can follow these steps:

### Step 1: Define the Angles
Let one angle be \( \theta \). Since the angles are supplementary, the other angle will be \( 180^\circ - \theta \).

### Step 2: Set Up the Equation
According to the problem, the two angles differ by \(36^\circ\). Therefore, we can write the equation:
\[ \theta - (180^\circ - \theta) = 36^\circ \]

### Step 3: Simplify the Equation
Now, simplify the left side of the equation:
\[ \theta - 180^\circ + \theta = 36^\circ \]
This simplifies to:
\[ 2\theta - 180^\circ = 36^\circ \]

### Step 4: Solve for \( \theta \)
Next, we will isolate \( \theta \):
\[ 2\theta = 36^\circ + 180^\circ \]
\[ 2\theta = 216^\circ \]
Now, divide both sides by 2:
\[ \theta = \frac{216^\circ}{2} = 108^\circ \]

### Step 5: Find the Other Angle
Now that we have \( \theta \), we can find the other angle:
\[ 180^\circ - \theta = 180^\circ - 108^\circ = 72^\circ \]

### Conclusion
The two supplementary angles are \( 108^\circ \) and \( 72^\circ \).

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