If `(5y+62)^(@), (22^(@)+y)` are supplementary, find y :

Options

A. `16^(@)`
B. `32^(@)`
C. `8^(@)`
D. `1^(@)`

Answer

To solve the problem, we need to find the value of \( y \) given that the angles \( (5y + 62)^\circ \) and \( (22 + y)^\circ \) are supplementary. Supplementary angles are two angles whose sum is equal to \( 180^\circ \).

### Step-by-Step Solution:

1. **Set Up the Equation**: Since the angles are supplementary, we can write the equation:
\[ (5y + 62) + (22 + y) = 180 \]

2. **Combine Like Terms**: Now, let's simplify the left side of the equation:
\[ 5y + 62 + 22 + y = 180 \]
Combine the \( y \) terms and the constant terms:
\[ 5y + y + 62 + 22 = 180 \]
This simplifies to:
\[ 6y + 84 = 180 \]

3. **Isolate the Variable**: Next, we need to isolate \( y \). Start by subtracting \( 84 \) from both sides:
\[ 6y = 180 - 84 \]
Calculate the right side:
\[ 6y = 96 \]

4. **Solve for \( y \)**: Now, divide both sides by \( 6 \):
\[ y = \frac{96}{6} \]
Simplifying this gives:
\[ y = 16 \]

### Final Answer:
Thus, the value of \( y \) is \( 16 \).

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