Question
In \( \triangle U V W, \overline{U V} \cong \overline{W U} \) and \( \mathrm{m} \angle W=51^{\circ} \). Find \( \mathrm{m} \angle U \)
Ask by Chavez Lewis. in the United States
Dec 17,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \angle U = 51^{\circ} \).
Solution
Given that in triangle \( \triangle UVW \), \( \overline{UV} \cong \overline{WU} \) and \( \angle W = 51^{\circ} \), we need to find the measure of angle \( \angle U \).
Since \( \overline{UV} \cong \overline{WU} \), we can conclude that triangle \( \triangle UVW \) is an isosceles triangle with \( \angle U = \angle W \).
Given that \( \angle W = 51^{\circ} \), we can substitute this value into the equation \( \angle U = \angle W \) to find the measure of angle \( \angle U \).
Therefore, \( \angle U = 51^{\circ} \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
In triangle \( U V W \), since \( \overline{U V} \cong \overline{W U} \), this indicates that triangle \( U V W \) is isosceles, with \( \angle U \) and \( \angle V \) being the base angles. The angles in a triangle sum up to \( 180^\circ \). Given that \( m\angle W = 51^\circ \), we can use this information to find the measures of \( \angle U \) and \( \angle V \): \[ m\angle U + m\angle V + m\angle W = 180^\circ \] \[ m\angle U + m\angle U + 51^\circ = 180^\circ \] \[ 2m\angle U + 51^\circ = 180^\circ \] \[ 2m\angle U = 180^\circ - 51^\circ \] \[ 2m\angle U = 129^\circ \] \[ m\angle U = \frac{129^\circ}{2} \] \[ m\angle U = 64.5^\circ \] Thus, \( m\angle U = 64.5^\circ \).
