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}`