Find the supplementary angle of each of the following angles:
`(3)/(7) " of " 280^(@)`

Answer

To find the supplementary angle of the given angle \( \frac{3}{7} \) of \( 280^\circ \), we will follow these steps:

### Step 1: Calculate \( \frac{3}{7} \) of \( 280^\circ \)
To find \( \frac{3}{7} \) of \( 280^\circ \), we multiply \( 280 \) by \( \frac{3}{7} \).

\[ \text{Angle} = \frac{3}{7} \times 280 \]

### Step 2: Simplify the multiplication
We can simplify the multiplication by first dividing \( 280 \) by \( 7 \):

\[ 280 \div 7 = 40 \]

Now, multiply \( 40 \) by \( 3 \):

\[ 40 \times 3 = 120 \]

So, \( \frac{3}{7} \) of \( 280^\circ \) is \( 120^\circ \).

### Step 3: Find the supplementary angle
The supplementary angle is found by subtracting the angle from \( 180^\circ \):

\[ \text{Supplementary angle} = 180^\circ - 120^\circ \]

### Step 4: Calculate the supplementary angle
Now, calculate the value:

\[ 180^\circ - 120^\circ = 60^\circ \]

Thus, the supplementary angle of \( \frac{3}{7} \) of \( 280^\circ \) is \( 60^\circ \).

### Final Answer
The supplementary angle is \( 60^\circ \).

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