Question

point z is the incenter of △srt. what is m∠ztb? 24° 31° 35° 62°

Explanation:

Step1: Recall incenter properties

The incenter \( Z \) is the intersection of angle bisectors, and \( ZB \perp ST \), \( ZA \perp SR \), \( ZC \perp RT \). So \( \angle ZBT = 90^\circ \).

Step2: Find \( \angle STR \)

First, find \( \angle SRT = 35^\circ + 35^\circ = 70^\circ \), \( \angle RST = 24^\circ + 24^\circ = 48^\circ \). In \( \triangle SRT \), \( \angle STR = 180^\circ - 70^\circ - 48^\circ = 62^\circ \).

Step3: Use angle bisector for \( \angle STR \)

Since \( Z \) is incenter, \( ZT \) bisects \( \angle STR \). So \( \angle ZTB=\frac{1}{2}\angle STR=\frac{62^\circ}{2}=31^\circ \).

Answer:

\( 31^\circ \) (corresponding to the option: \( 31^\circ \))