To determine the measure of angle m∠QOB where O is the incenter of triangle ABC, we first need to understand the properties of the incenter. The incenter is the point where the angle bisectors of a triangle meet, and it is equidistant from all sides of the triangle.
Let’s denote the angles of triangle ABC as follows: m∠A, m∠B, and m∠C. The angle formed at the incenter related to these angles can be calculated using the formula:
m∠QOB = 90° + 0.5 * m∠C
This implies that the measure of angle QOB depends on the angle C of triangle ABC. However, without specific information about the angles of triangle ABC, we cannot determine the exact measure of m∠QOB at this point. But we can analyze the given options: 30°, 60°, 75°, or 90°.
For example, if angle C is 60°, substituting it into our equation gives:
m∠QOB = 90° + 0.5 * 60° = 90° + 30° = 120°
So, the ratio may yield different results based on m∠C. Therefore, we need the angle measures of triangle ABC to pinpoint the exact value of m∠QOB.
Based on typical angle distributions for triangles, if we assume that m∠C leads to a 30° or 60° total angle at the incenter, it would indicate possible options depending on the configuration of triangles. Ultimately, angle m∠QOB will vary by triangle shape, leading to no single answer fitting all scenarios.