Question

if rs = ru = 11, m∠rts = 2y - 2°, and m∠rtu = y, what is m∠stu?

m∠stu = □°

Explanation:

Step1: Use the Angle Bisector Theorem

Since \(RS = RU = 11\) and \(TS\perp RS\), \(TU\perp RU\), by the converse of the angle bisector theorem, \(RT\) bisects \(\angle STU\). So \(m\angle RTS=m\angle RTU\).
Set up the equation \(2y - 2=y\).

Step2: Solve for \(y\)

Subtract \(y\) from both sides: \(2y-y - 2=y - y\), which gives \(y-2 = 0\).
Add \(2\) to both sides: \(y-2 + 2=0 + 2\), so \(y = 2\).

Step3: Find \(m\angle STU\)

Since \(m\angle STU=m\angle RTS+m\angle RTU\), and \(m\angle RTS = 2y-2\), \(m\angle RTU=y\). Substitute \(y = 2\) into the expressions.
\(m\angle RTS=2\times2-2=2^{\circ}\), \(m\angle RTU = 2^{\circ}\). Then \(m\angle STU=2 + 2=4^{\circ}\).

Answer:

\(4\)