Answer :
Given the problem involves finding the sum of the interior angles of a convex [tex]$n$[/tex]-gon where [tex]$n$[/tex] is the number of sides of the polygon.
Step-by-step, here's the solution:
1. Identify the number of sides:
- For a quadrilateral, the number of sides [tex]$n = 4$[/tex].
2. Recall the formula for the sum of interior angles for a convex [tex]$n$[/tex]-gon:
- The formula is \( 180^{\circ}(n - 2) \).
3. Substitute \( n = 4 \) into the formula:
- \( 180^{\circ}(n - 2) = 180^{\circ}(4 - 2) \).
4. Simplify the expression:
- \( 180^{\circ}(4 - 2) = 180^{\circ} \times 2 = 360^{\circ} \).
Thus, the sum of the interior angles for a quadrilateral [tex]$L M N P$[/tex] is \( 360^{\circ} \).
Since this sum of angles represents \( x \):
[tex]\[ x = 360^{\circ} \][/tex]
So, the value of \( x \) is:
[tex]\[ x = 360^{\circ} \][/tex]
Step-by-step, here's the solution:
1. Identify the number of sides:
- For a quadrilateral, the number of sides [tex]$n = 4$[/tex].
2. Recall the formula for the sum of interior angles for a convex [tex]$n$[/tex]-gon:
- The formula is \( 180^{\circ}(n - 2) \).
3. Substitute \( n = 4 \) into the formula:
- \( 180^{\circ}(n - 2) = 180^{\circ}(4 - 2) \).
4. Simplify the expression:
- \( 180^{\circ}(4 - 2) = 180^{\circ} \times 2 = 360^{\circ} \).
Thus, the sum of the interior angles for a quadrilateral [tex]$L M N P$[/tex] is \( 360^{\circ} \).
Since this sum of angles represents \( x \):
[tex]\[ x = 360^{\circ} \][/tex]
So, the value of \( x \) is:
[tex]\[ x = 360^{\circ} \][/tex]
