The measure of angles of a quadrilateral are `(x+20)^(0)`,`(x-20^(0))^(0),(2x+5)^(0)` & `(2x-5)^(0).` find the value of x.

Answer

To find the value of \( x \) in the given quadrilateral with angles \( (x + 20)^\circ \), \( (x - 20)^\circ \), \( (2x + 5)^\circ \), and \( (2x - 5)^\circ \), we will follow these steps:

### Step 1: Write the equation for the sum of angles in a quadrilateral
The sum of the interior angles of a quadrilateral is always \( 360^\circ \). Therefore, we can set up the equation:
\[ (x + 20) + (x - 20) + (2x + 5) + (2x - 5) = 360 \]

### Step 2: Simplify the equation
Now, we will combine like terms in the equation:
\[ x + 20 + x - 20 + 2x + 5 + 2x - 5 = 360 \]
This simplifies to:
\[ x + x + 2x + 2x + 20 - 20 + 5 - 5 = 360 \]
Combining the \( x \) terms:
\[ 6x + 0 = 360 \]
So, we have:
\[ 6x = 360 \]

### Step 3: Solve for \( x \)
To find \( x \), divide both sides of the equation by 6:
\[ x = \frac{360}{6} \]
Calculating this gives:
\[ x = 60 \]

### Final Answer
The value of \( x \) is \( 60 \).

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