In triangle, U, V, W, comma△UVW, start overline, U, V, end overline, \cong, start overline, W, U, end overline
UV
≅
WU
and m, angle, W, equals, 38, degrees, .m∠W=38
∘
. Find m, angle, U, .m∠U.
We have that the two sides UV and WU are congruent, meaning |UV| = |WU|.
Since UV and WU are congruent, we know that angle U is congruent to angle V.
So m∠U = m∠V.
We also know that m∠W = 38∘.
Since the sum of the angles in a triangle is 180∘, we can subtract the measures of angles U and V from 180∘ to find the measure of angle W.
180∘ - m∠U - m∠V = m∠W
180∘ - m∠U - m∠U = 38∘
180∘ - 2m∠U = 38∘
Now we can solve for m∠U.
180∘ - 2m∠U = 38∘
-2m∠U = 38∘ - 180∘
-2m∠U = -142∘
m∠U = -142∘ / -2
m∠U = 71∘
So, m∠U = 71∘.