Certainly! Let's solve this step-by-step.
1. Identify the external angles of the polygon:
- The external angles given are [tex]\(30^\circ\)[/tex], [tex]\(40^\circ\)[/tex], [tex]\(120^\circ\)[/tex], and [tex]\(142^\circ\)[/tex].
- The fifth angle is unknown and denoted by [tex]\(y\)[/tex].
2. Recall the property of external angles of a polygon:
- The sum of the external angles of any polygon is always [tex]\(360^\circ\)[/tex].
3. Sum the known external angles:
- Adding the given angles, we get:
[tex]\[
30^\circ + 40^\circ + 120^\circ + 142^\circ = 332^\circ
\][/tex]
4. Calculate the unknown external angle [tex]\(y\)[/tex]:
- To find [tex]\(y\)[/tex], we subtract the sum of the known angles from the total sum of external angles:
[tex]\[
y = 360^\circ - 332^\circ = 28^\circ
\][/tex]
So, the value of [tex]\(y\)[/tex] is [tex]\(28^\circ\)[/tex].
