In triangle, V, W, X, comma△VWX, start overline, W, X, end overline, \cong, start overline, V, W, end overline
WX
≅
VW
and m, angle, V, equals, 51, degrees, .m∠V=51
∘
. Find m, angle, X, .m∠X.
Since WX ≅ VW, we know that triangle VWX is an isosceles triangle. In an isosceles triangle, the base angles are congruent. Therefore, we can deduce that m∠W = m∠X.
Given that m∠V = 51°, we can apply the Triangle Angle Sum Theorem to find m∠X.
Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180°.
m∠V + m∠W + m∠X = 180°
Substituting the known values:
51° + m∠W + m∠W = 180°
2m∠W = 180° - 51°
2m∠W = 129°
m∠W = 129° / 2
m∠W = 64.5°
Since m∠W = m∠X, m∠X is also 64.5°.