Angles `x` & `y` forms a linear pair and `2y-x=30^@`, the value of `y` is

Options

A. `70^@`
B. `110^@`
C. `210^@`
D. `60^@`

Answer

To solve for the value of angle \( y \) given that angles \( x \) and \( y \) form a linear pair and the equation \( 2y - x = 30^\circ \), we can follow these steps:

### Step 1: Understand the properties of linear pairs
Since angles \( x \) and \( y \) form a linear pair, we know that:
\[ x + y = 180^\circ \]
This is because the sum of angles on a straight line is \( 180^\circ \).

### Step 2: Express \( x \) in terms of \( y \)
From the equation \( x + y = 180^\circ \), we can express \( x \) as:
\[ x = 180^\circ - y \]

### Step 3: Substitute \( x \) into the second equation
We are given the equation:
\[ 2y - x = 30^\circ \]
Now, substitute \( x \) from Step 2 into this equation:
\[ 2y - (180^\circ - y) = 30^\circ \]

### Step 4: Simplify the equation
Now simplify the equation:
\[ 2y - 180^\circ + y = 30^\circ \]
Combine like terms:
\[ 3y - 180^\circ = 30^\circ \]

### Step 5: Solve for \( y \)
Now, add \( 180^\circ \) to both sides:
\[ 3y = 30^\circ + 180^\circ \]
\[ 3y = 210^\circ \]
Now, divide both sides by 3:
\[ y = \frac{210^\circ}{3} = 70^\circ \]

Thus, the value of \( y \) is \( 70^\circ \).