in $ \triangle tuv, m \angle t = 105 ^ { \circ } $ and $ m \angle u = 11 ^ { \circ } $. which statement about the sides of $ \triangle tuv $ must be true?
answer
$ \bigcirc uv tu vt $
$ \bigcirc uv vt tu $
$ \bigcirc tu uv vt $
$ \bigcirc tu vt uv $
$ \bigcirc vt tu uv $
$ \bigcirc vt uv tu $

Question

in $ \triangle tuv, m \angle t = 105 ^ { \circ } $ and $ m \angle u = 11 ^ { \circ } $. which statement about the sides of $ \triangle tuv $ must be true?
answer
$ \bigcirc uv > tu > vt $
$ \bigcirc uv > vt > tu $
$ \bigcirc tu > uv > vt $
$ \bigcirc tu > vt > uv $
$ \bigcirc vt > tu > uv $
$ \bigcirc vt > uv > tu $

Accepted Answer

# Answer:
UV > VT > TU

# Explanation:
## Step1: Find the measure of angle V
The sum of angles in a triangle is $180^{\circ}$. So, $m\angle V=180^{\circ}-m\angle T - m\angle U$.
Substituting the given values: $m\angle V = 180^{\circ}-105^{\circ}-11^{\circ}=64^{\circ}$.

## Step2: Relate angles and sides
In a triangle, the larger the angle, the longer the side opposite it.
Since $m\angle T = 105^{\circ}$, $m\angle V=64^{\circ}$, $m\angle U = 11^{\circ}$, and the side opposite $\angle T$ is $UV$, the side opposite $\angle V$ is $TU$, the side opposite $\angle U$ is $VT$.
So, $UV>VT>TU$ (because $105^{\circ}>64^{\circ}>11^{\circ}$).

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QUESTION IMAGE

Question

Explanation:

Step1: Find the measure of angle V

Step2: Relate angles and sides

Answer: