Question

find all unknown measure in each pair of similar trianglea

Answer 1

We have the next two triangles

And we must find the missing angles.

Since they are similar triangles we know that their angles are congruent. That means,

$\begin{gathered} \angle V\cong\angle Y \\ \angle T\cong\angle X \\ \angle W\cong\angle Z \end{gathered}$

Using that,

$\angle V=28^{\circ},\text{ then }\angle Y=28^{\circ}$$\angle X=74^{\circ},\text{ then }\angle T=74^{\circ}$

Now, to find the las angle of each triangle we must use that the interior angles of a triangl add up to 180°

$\begin{gathered} 28^{^{\circ}^{}}+74^{\circ}+\angle Z=180^{\circ} \\ \angle Z=180^{\circ}-(28^{^{\circ}}+74^{\circ}) \\ \angle Z=78^{\circ} \end{gathered}$

Finally,

$\angle Z=78^{\circ},\text{ then }\angle W=78^{\circ}$

ANSWER:

$\begin{gathered} \angle T=74^{\circ} \\ \angle W=78^{\circ} \\ \angle Y=28^{\circ} \\ \angle Z=78^{\circ} \end{gathered}$