student.freckle.com/assignments/targeted/147307992/session Mathletics: powerin... Summit Learning Google Slides Rapididentity Classes Apple Music Clever । \( \overline{S U} \) is the bisector of \( \angle R S T \). If \( m \angle R S T=7 x+6 \) and \( m \angle T S U=4 x-2 \), what is \( m \angle R S U \) ?

To determine the measure of \( \angle R S U \), let's analyze the given information step by step. 1. **Understanding the Bisector:** - \( \overline{S U} \) is the **bisector** of \( \angle R S T \). This means it divides \( \angle R S T \) into two **equal** angles: \[ \angle R S U = \angle T S U \] 2. **Given Measurements:** - \( m \angle R S T = 7x + 6 \) - \( m \angle T S U = 4x - 2 \) 3. **Setting Up the Equation:** - Since \( \overline{S U} \) bisects \( \angle R S T \): \[ \angle R S U = \angle T S U = 4x - 2 \] - The entire angle \( \angle R S T \) is the sum of these two equal angles: \[ m \angle R S T = \angle R S U + \angle T S U \] \[ 7x + 6 = (4x - 2) + (4x - 2) \] \[ 7x + 6 = 8x - 4 \] 4. **Solving for \( x \):** \[ 7x + 6 = 8x - 4 \] \[ 6 + 4 = 8x - 7x \] \[ 10 = x \] 5. **Finding \( m \angle R S U \):** \[ m \angle R S U = 4x - 2 = 4(10) - 2 = 40 - 2 = 38^\circ \] **Answer:** \( \angle R S U = 38^\circ \)