Question

$\triangle uvw \sim \triangle pqr$. what is $m\angle v$?
(there are two triangles in the image: $\triangle uvw$ with angles at $u$: $39^\circ$, at $w$: $92^\circ$; $\triangle pqr$ with angles at $q$: $49^\circ$, at $r$: $92^\circ$, at $p$: $39^\circ$)

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle UVW\sim\triangle PQR\), corresponding angles are equal.

Step2: Use the angle - sum property of a triangle

In a triangle, the sum of interior angles is \(180^{\circ}\). For \(\triangle UVW\), we know \(\angle U = 39^{\circ}\), \(\angle W=92^{\circ}\). Let \(\angle V=x\). Then \(x + 39^{\circ}+92^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

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Answer:

\(49^{\circ}\)