In triangle, V, W, X, comma△VWX, start overline, V, W, end overline, \cong, start overline, X, V, end overline
VW
≅
XV
and m, angle, V, equals, 47, degrees, .m∠V=47
∘
. Find m, angle, X, .m∠X.
Since triangle VWX is an isosceles triangle with VW ≅ XV, we know that angle W and angle X are congruent. Therefore, we can say that m∠X = m∠W.
We also know that m∠V = 47°. Since the sum of the angles in a triangle is always 180°, we can write the equation:
m∠V + m∠W + m∠X = 180°
Substituting m∠V with 47° and m∠X with m∠W, we have:
47° + m∠W + m∠W = 180°
Combining like terms, we have:
2m∠W + 47° = 180°
Subtracting 47° from both sides of the equation, we get:
2m∠W = 180° - 47°
2m∠W = 133°
Dividing both sides of the equation by 2, we find:
m∠W = 133° / 2
m∠W = 66.5°
Since angle X is congruent to angle W, we can conclude that:
m∠X = m∠W = 66.5°