U
△WFI≅△EAU. If
m
∠
F
=
7
7
∘
m∠F=77
∘
and
m
∠
W
=
3
7
∘
m∠W=37
∘
, find
m
∠
U
m∠U.
We know that the two triangles △WFI and △EAU are congruent, so their corresponding angles are equal. Thus,
m∠U = m∠A
We are given that m∠F = 77, so
m∠WFI = 180 - m∠F - m∠W = 66
Since △WFI is congruent to △EAU, we know that m∠A = m∠WFI, so
m∠U = m∠A = m∠WFI = 66
Therefore, m∠U is 66 degrees.
Since △WFI ≅ △EAU, we can use the corresponding angles property to find the measure of angle U.
Corresponding angles in congruent triangles are equal, so we have:
m∠W = m∠E
m∠F = m∠A
Given that m∠W = 37° and m∠F = 77°, we can substitute those values into the corresponding angles to find the measure of angle U:
m∠U = m∠E = m∠W = 37°
Therefore, m∠U is 37°.