Question

the wind changes again and the weathervane turns another 70°. now it points directly south. which angle is adjacent to ∠tvs? ∠nvt what is m∠nvs? m∠nvs = °

Explanation:

Step1: Analyze the diagram and angles

From the diagram, we know that \( \angle NVS \) is formed by the North - South line and the angle between \( NV \) and \( SV \). Also, we know that the weathervane's movements and the angles given. We can see that \( \angle NVS \) is a straight - line angle? Wait, no. Wait, the North (\( N \)) and South (\( S \)) are opposite directions, so the angle between \( NV \) (towards North) and \( SV \) (towards South) should be a straight angle? But wait, there are other angles. Wait, actually, looking at the diagram, we can see that the angle \( \angle NVT = 110^{\circ}\) and \( \angle TVS=70^{\circ}\). To find \( m\angle NVS \), we can add the measures of \( \angle NVT \) and \( \angle TVS \) because they are adjacent angles forming \( \angle NVS \).

Step2: Calculate \( m\angle NVS \)

We know that \( m\angle NVT = 110^{\circ}\) and \( m\angle TVS = 70^{\circ}\). Then \( m\angle NVS=m\angle NVT + m\angle TVS\). Substituting the values, we get \( m\angle NVS=110^{\circ}+70^{\circ}\).
\( 110 + 70=180 \), so \( m\angle NVS = 180^{\circ}\)? Wait, no, that can't be. Wait, wait, North and South are opposite, so the angle between North and South is \( 180^{\circ}\). And the two angles \( \angle NVT \) and \( \angle TVS \) are adjacent and together make up \( \angle NVS \). So \( m\angle NVS=110^{\circ}+70^{\circ}=180^{\circ}\). Wait, but let's check again. The weathervane first turned to some position, then another \( 70^{\circ}\) to South. So the angle from North to T is \( 110^{\circ}\), from T to S is \( 70^{\circ}\), so from North to South is \( 110 + 70 = 180^{\circ}\).

Answer:

\( 180 \)