Angles of a triangle are `(y + 36)^@, (2y - 14)^@ and (y - 22)^@`. What is the value (in degrees) of 2y?

Options

A. 45
B. 70
C. 90
D. 100

Answer

To solve the problem, we need to find the value of \(2y\) given the angles of a triangle as \((y + 36)^\circ\), \((2y - 14)^\circ\), and \((y - 22)^\circ\).

### Step-by-Step Solution:

1. **Write the equation for the sum of the angles in a triangle**:
The sum of the angles in a triangle is always \(180^\circ\). Therefore, we can set up the equation:
\[ (y + 36) + (2y - 14) + (y - 22) = 180 \]

2. **Combine like terms**:
Now, we will combine the terms on the left side of the equation:
\[ y + 36 + 2y - 14 + y - 22 = 180 \]
This simplifies to:
\[ (y + 2y + y) + (36 - 14 - 22) = 180 \]
Which further simplifies to:
\[ 4y + 0 = 180 \]
Therefore, we have:
\[ 4y = 180 \]

3. **Solve for \(y\)**:
Now, divide both sides of the equation by \(4\):
\[ y = \frac{180}{4} = 45 \]

4. **Calculate \(2y\)**:
Now that we have the value of \(y\), we can find \(2y\):
\[ 2y = 2 \times 45 = 90 \]

### Final Answer:
Thus, the value of \(2y\) is \(90^\circ\).