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The sum of the interior angle measures of a convex \(n\)-gon is \(180^{\circ}(n-2)\).

Since this is a quadrilateral, \(n=4\). So, the sum for \(L M N P\) is:

[tex]\[
180^{\circ}(n-2)=180^{\circ}(4-2)=180^{\circ}(2)=360^{\circ}
\][/tex]

What is the value of \(x\)?

Enter your answer in the box.

[tex]\[
x=\square^{\circ}
\][/tex]

Sagot :

GinnyAnswer
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]
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