Question

1. find ( mangle v ).
2. use tools describe how to construct the image of ( \triangle abc ) under a dilation with center ( c ) and scale factor 3. state what strategy and tool you will use to answer the question, explain your choice, and then find the answer.

Explanation:

Step1: Determine similarity of triangles

Since the triangles are right - angled and have corresponding angles equal (by the AA similarity criterion, as right angles are equal and the other non - right angles are corresponding), \(\triangle TUV\sim\triangle QRS\).

Step2: Use angle - sum property of similar triangles

In a right - angled triangle, the sum of the two non - right angles is \(90^{\circ}\). In \(\triangle QRS\), \(\angle S = 74^{\circ}\), \(\angle R=90^{\circ}\). For \(\triangle TUV\), \(\angle U = 90^{\circ}\).
Since \(\triangle TUV\sim\triangle QRS\), \(\angle V\) and \(\angle S\) are corresponding non - right angles.
We know that in a right - angled triangle \(A + B=90^{\circ}\) (where \(A\) and \(B\) are non - right angles).
In \(\triangle QRS\), \(\angle Q+\angle S = 90^{\circ}\), and in \(\triangle TUV\), \(\angle T+\angle V=90^{\circ}\). Because of similarity \(\angle V=\angle Q\)
We can also calculate using the fact that for similar triangles, corresponding angles are equal.
In \(\triangle QRS\), \(\angle Q=90^{\circ}- 74^{\circ}\)

$$ \angle Q=16^{\circ} $$

Since \(\triangle TUV\sim\triangle QRS\), \(m\angle V = 16^{\circ}\)

Answer:

\(m\angle V=16^{\circ}\)