Question

in $delta tuv$, $mangle t = 105^{circ}$ and $mangle u = 11^{circ}$. which statement about the sides of $delta tuv$ must be true? answer: $uv > tu > vt$, $uv > vt > tu$, $tu > uv > vt$, $tu > vt > uv$, $vt > tu > uv$, $vt > uv > tu$

Explanation:

Step1: Find angle V

In a triangle, the sum of interior angles is 180°. So, $m\angle V=180^{\circ}-m\angle T - m\angle U=180^{\circ}- 105^{\circ}-11^{\circ}=64^{\circ}$.

Step2: Apply angle - side relationship

In a triangle, the side opposite the largest angle is the longest and the side opposite the smallest angle is the shortest. Since $\angle T = 105^{\circ}$ (largest), $\angle V=64^{\circ}$, and $\angle U = 11^{\circ}$ (smallest), the side opposite $\angle T$ is VT, the side opposite $\angle V$ is TU, and the side opposite $\angle U$ is UV. So, VT > TU > UV.

Answer:

VT > TU > UV