The angles of a quadrilateral are `(x+20, (x-20), (2x+5), (2x-5)`. Find the value of x.

Answer

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

### Step 1: Write the equation for the sum of angles in a quadrilateral.
The sum of the angles in a quadrilateral is always equal to \( 360^\circ \). 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:
\[ x + 20 + x - 20 + 2x + 5 + 2x - 5 = 360 \]
The \( +20 \) and \( -20 \) cancel each other out, as do \( +5 \) and \( -5 \):
\[ x + x + 2x + 2x = 360 \]
This simplifies to:
\[ 6x = 360 \]

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

### Conclusion:
The value of \( x \) is \( 60 \).

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