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 \( m \angle R S U \) ?
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To find \( m \angle R S U \), we first need to understand that since \( \overline{S U} \) is the bisector of \( \angle R S T \), the two angles \( m \angle R S U \) and \( m \angle T S U \) are equal. Thus, we can set up the equation: \[ m \angle R S T = m \angle R S U + m \angle T S U \] \[ 7x + 6 = m \angle R S U + (4x - 2) \] Now, since \( m \angle R S U = m \angle T S U \): \[ 7x + 6 = 2(4x - 2) \] Solving this will lead us to find the measure of \( m \angle R S U \): 1. Distribute: \[ 7x + 6 = 8x - 4 \] 2. Rearranging gives: \[ -x + 6 = -4 \] 3. Thus: \[ -x = -10 \quad \Rightarrow \quad x = 10 \] Now substituting \( x \) back into \( m \angle R S U = 4x - 2 \): \[ m \angle R S U = 4(10) - 2 = 40 - 2 = 38 \] Therefore, \( m \angle R S U = 38^\circ \).
