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To determine the measure of angle \(B\) in triangle \(ABC\), we can use the fact that the sum of the angles in any triangle is always \(180^\circ\).

The angles provided are:

- Angle \(A = 28.7^\circ\)
- Angle \(C = 116.1^\circ\)

Thus, we can calculate angle \(B\) using the equation:
\[
B = 180^\circ - A - C
\]

Now let's compute this.The measure of angle \( B \) is approximately \( 35.2^\circ \).

Would you like further clarification or more details on this solution?

Here are five related questions to expand on this topic:

1. How would you calculate the sides of the triangle using the Law of Sines?
2. What are the rules for solving oblique triangles?
3. How do you verify the sum of angles in a triangle?
4. What is the difference between using the Law of Sines and the Law of Cosines for solving triangles?
5. Can you solve for the remaining sides of this triangle with the given information?

**Tip:** In any triangle, always verify that the sum of all angles equals \(180^\circ\), as it's a fundamental property of triangles.

Determine the remaining sides and angles of triangle ABC. What is the measure of angle B?

Find the measure of angle B in triangle ABC using the angle sum theorem. With given angles A = 28.7° and C = 116.1°, calculate angle B through subtraction from 180°. This problem is suitable for high school students learning geometry.

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