Question

what is m∠vsw? m∠vsw = °

Explanation:

Step1: Recall total angle around a point

The total angle around a point (like point \( S \)) is \( 360^\circ \).

Step2: Sum known angles

We know angles: \( 140^\circ \), two \( 60^\circ \) angles. Let \( \angle VSW = x \). So \( 140 + 60 + 60 + x = 360 \).

Step3: Solve for \( x \)

Calculate sum of known angles: \( 140 + 60 + 60 = 260 \). Then \( x = 360 - 260 = 100 \). Wait, no—wait, looking at the diagram, \( \angle VSW \) is adjacent? Wait, no, maybe I misread. Wait, the lines from \( S \): \( V \) to \( S \), \( W \) to \( S \), and the other angles. Wait, actually, the angles around \( S \): \( \angle VSU = 140^\circ \), \( \angle US T = 60^\circ \), \( \angle TSW = 60^\circ \), and \( \angle WSV \) (which is \( \angle VSW \))? Wait, no, total around \( S \) is \( 360 \). So \( 140 + 60 + 60 + \angle VSW = 360 \). So \( 260 + \angle VSW = 360 \), so \( \angle VSW = 100 \)? Wait, no, maybe the diagram is: \( V \) is a line, \( W \) is another, with angles between \( W \) and \( T \) is \( 60 \), \( T \) and \( U \) is \( 60 \), \( U \) and \( V \) is \( 140 \). So from \( W \) to \( V \): the angles between \( W-T \) (60), \( T-U \) (60), \( U-V \) (140). Wait, no, that can't be. Wait, maybe the angle \( \angle VSW \) is calculated as \( 360 - 140 - 60 - 60 \)? Wait, 360 - 140 is 220, 220 - 60 is 160, 160 - 60 is 100? Wait, but maybe I made a mistake. Wait, no, let's check again. The diagram: point \( S \), with four lines: \( SV \), \( SU \), \( ST \), \( SW \). Angles: \( \angle VSU = 140^\circ \), \( \angle US T = 60^\circ \), \( \angle TSW = 60^\circ \), and \( \angle WSV \) (which is \( \angle VSW \)). So sum of angles: \( 140 + 60 + 60 + \angle VSW = 360 \). So \( 260 + \angle VSW = 360 \), so \( \angle VSW = 100^\circ \). Wait, but maybe the problem is simpler. Wait, no, maybe the angle \( \angle VSW \) is between \( SV \) and \( SW \), and the other angles are \( 60 \), \( 60 \), \( 140 \). So total around \( S \): 140 + 60 + 60 + x = 360. So x = 360 - 140 - 60 - 60 = 100. So \( m\angle VSW = 100^\circ \)? Wait, but let me check again. Wait, maybe I misread the angles. The diagram shows: from \( S \), \( V \) is up, \( U \) is to the right-down, \( T \) is to the left-down, \( W \) is to the left. So angles: between \( U \) and \( V \): 140, \( U \) and \( T \): 60, \( T \) and \( W \): 60, and \( W \) and \( V \):? So 140 + 60 + 60 + x = 360. So x = 100. Yes, that makes sense.

Answer:

\( 100 \)