Problem Analysis:
The image shows a pentagon with four of its interior angles given: \(120^\circ\), \(112^\circ\), \(118^\circ\), and \(130^\circ\). The fifth angle is labeled as \(x^\circ\). The task is to find the value of \(x\).
Key Concepts:
1.
Sum of Interior Angles of a Polygon:
The sum of the interior angles of a polygon with \(n\) sides is given by the formula:
\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\]
For a pentagon (\(n = 5\)):
\[
\text{Sum of interior angles} = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ
\]
2.
Using the Given Angles:
We know four of the five interior angles of the pentagon. Let the fifth angle be \(x\). The sum of all five angles must equal \(540^\circ\):
\[
120^\circ + 112^\circ + 118^\circ + 130^\circ + x = 540^\circ
\]
Step-by-Step Solution:
1.
Calculate the Sum of the Known Angles:
\[
120^\circ + 112^\circ + 118^\circ + 130^\circ = 480^\circ
\]
2.
Set Up the Equation:
The sum of all five angles is \(540^\circ\). Therefore:
\[
480^\circ + x = 540^\circ
\]
3.
Solve for \(x\):
\[
x = 540^\circ - 480^\circ = 60^\circ
\]
Final Answer:
\[
\boxed{60}
\]
Parent Tip: Review the logic above to help your child master the concept of angles of polygons worksheets.
