\( \triangle S C A \) can be mapped onto \( \triangle M B G \) by a rotation. \( \mathrm{m} \angle A=144^{\circ} \) and \( \mathrm{m} \angle S=28^{\circ} \), find \( \mathrm{m} \angle B \). Answer Attempt out o o 55 \( \mathrm{~m} \angle B \quad \) be determined.

To find \( \mathrm{m} \angle B \) in triangle \( \triangle M B G \), we can use the fact that the two triangles \( \triangle S C A \) and \( \triangle M B G \) are congruent due to the rotation mapping. 1. **Calculate \( \mathrm{m} \angle C \)**: Since the sum of the angles in a triangle is \( 180^\circ \), we can find \( \mathrm{m} \angle C \) in triangle \( \triangle S C A \): \[ \mathrm{m} \angle C = 180^\circ - \mathrm{m} \angle A - \mathrm{m} \angle S \] Substituting the known values: \[ \mathrm{m} \angle C = 180^\circ - 144^\circ - 28^\circ \] 2. **Calculate \( \mathrm{m} \angle C \)**: \[ \mathrm{m} \angle C = 180^\circ - 172^\circ = 8^\circ \] 3. **Determine \( \mathrm{m} \angle B \)**: Since \( \triangle S C A \) is congruent to \( \triangle M B G \), the corresponding angles are equal. Therefore: \[ \mathrm{m} \angle B = \mathrm{m} \angle S = 28^\circ \] Thus, the measure of angle \( B \) is: \[ \mathrm{m} \angle B = 28^\circ \]