Question

in δtuv, uv = 12, vt = 13, and tu = 4. which statement about the angles of δtuv must be true? answer m∠v > m∠u > m∠t m∠t > m∠v > m∠u m∠u > m∠t > m∠v m∠t > m∠u > m∠v m∠u > m∠v > m∠t m∠v > m∠t > m∠u

Explanation:

Step1: Recall angle - side relationship

In a triangle, the larger the side length, the larger the measure of the opposite angle.

Step2: Identify opposite angles

In \(\triangle TUV\), side \(VT = 13\) is opposite \(\angle U\), side \(UV=12\) is opposite \(\angle T\), and side \(TU = 4\) is opposite \(\angle V\).

Step3: Compare side lengths

We have \(VT>UV>TU\) (since \(13 > 12>4\)).

Step4: Determine angle - size relationship

So, \(m\angle U>m\angle T>m\angle V\) according to the angle - side relationship in a triangle.

Answer:

\(m\angle U > m\angle T > m\angle V\)