Question

1. what is the measure of angle x? 60° 90° 45° 30°

Explanation:

Step1: Analyze triangle RVT

In right triangle \( RVT \), \( RV = 16 \) cm, and we can find some relationships. Also, note the right angles at \( V \) and \( U \).

Step2: Analyze triangle SVU

In triangle \( SVU \), we know one angle is \( 45^\circ \) and it's a right triangle? Wait, maybe better to look at triangle \( RVT \). The length \( RV = 16 \), and the segment \( VU = 8 \), which is half of \( RV \)? Wait, no, \( VU = 8 \), \( RV = 16 \). Wait, maybe triangle \( RVS \) and \( TVS \)? Wait, another approach: in triangle \( RVT \), angle at \( R \) is \( 60^\circ \), so angle at \( T \) (which is \( x \)): wait, maybe using the 30-60-90 triangle properties? Wait, \( RV = 16 \), and if we consider the side \( VU = 8 \), which is half of \( RV \). Wait, maybe triangle \( RVU \)? No, let's think about the angles. Wait, the triangle \( RSV \): angle at \( R \) is \( 60^\circ \), right angle at \( V \), so angle at \( S \) (in triangle \( RSV \)) would be \( 30^\circ \)? Wait, no, maybe the key is that in triangle \( RVT \), \( RV = 16 \), and the height \( SU \) or something? Wait, maybe the angle \( x \) is \( 30^\circ \)? Wait, let's check the options. The options are \( 60^\circ \), \( 90^\circ \), \( 45^\circ \), \( 30^\circ \). Wait, in a 30-60-90 triangle, the sides are in the ratio \( 1 : \sqrt{3} : 2 \). If \( RV = 16 \) (the longer leg, opposite \( 60^\circ \)), then the shorter leg (opposite \( 30^\circ \)) would be \( 8 \), which matches \( VU = 8 \). So angle at \( T \) ( \( x \)) should be \( 30^\circ \), because in triangle \( RVT \), angles sum to \( 180^\circ \), right angle at \( V \), angle at \( R \) is \( 60^\circ \), so angle at \( T \) is \( 180 - 90 - 60 = 30^\circ \).

Answer:

\( 30^\circ \) (the option with \( 30^\circ \))