Question

if qr = qt = 75, m∠qsr = 2a, and m∠qst = 3a - 21°, what is m∠qst?

m∠qst = □°

Explanation:

Step1: Identify angle bisector

Since \( QR = QT = 75 \) and \( \angle SRQ=\angle STQ = 90^\circ \), \( SQ \) bisects \( \angle RST \). So \( m\angle QSR=m\angle QST \).

Step2: Set up equation

Set \( 2a=3a - 21^\circ \).

Step3: Solve for \( a \)

Subtract \( 2a \) from both sides: \( 0=a - 21^\circ \), so \( a = 21^\circ \).

Step4: Calculate \( m\angle QST \)

Substitute \( a = 21^\circ \) into \( 3a-21^\circ \): \( 3\times21^\circ-21^\circ=63^\circ - 21^\circ = 42^\circ \).

Answer:

\( 42 \)