Let's determine the correct equation step-by-step, knowing that one of the interior angles of the triangle is \(48^\circ\) and the other two angles are congruent.
1. Sum of Interior Angles:
- The sum of the interior angles of any triangle is always \(180^\circ\).
2. Representation of Angles:
- Let's denote the measure of each of the congruent angles as \(x\).
3. Equation Setup:
- Given that one angle is \(48^\circ\) and the other two angles are congruent, the equation representing the sum of the angles in the triangle will be:
[tex]\[
48^\circ + x + x = 180^\circ
\][/tex]
- Simplifying this equation:
[tex]\[
48^\circ + 2x = 180^\circ
\][/tex]
4. Correct Equation:
- Rearrange the simplified equation to isolate \(2x\):
[tex]\[
2x + 48 = 180
\][/tex]
Thus, the equation that could be used to determine the degree measure of one of the congruent angles is:
[tex]\[
2x + 48 = 180
\][/tex]
This matches the fourth option provided:
[tex]\[
2x + 48 = 180
\][/tex]
