Question

question 6 unique id: 0935 △wfi≅△eau. if m∠f = 77° and m∠w = 37°, find m∠u. answer m∠u cannot be determined.

Explanation:

Step1: Recall congruent - triangle property

If $\triangle WFI\cong\triangle EAU$, then corresponding angles are equal. $\angle W$ corresponds to $\angle E$, $\angle F$ corresponds to $\angle A$, and $\angle I$ corresponds to $\angle U$.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. In $\triangle WFI$, we know $m\angle F = 77^{\circ}$ and $m\angle W=37^{\circ}$. Let $m\angle I = x$. Then $m\angle W + m\angle F+m\angle I=180^{\circ}$.
So, $37^{\circ}+77^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

First, add the known angles: $37^{\circ}+77^{\circ}=114^{\circ}$. Then $x=180^{\circ}-114^{\circ}=66^{\circ}$. Since $\angle I$ and $\angle U$ are corresponding angles in congruent triangles $\triangle WFI$ and $\triangle EAU$, $m\angle U = 66^{\circ}$.

Answer:

$66^{\circ}$