Question

properties of isosceles triangles
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question
in $\triangle uwv$, $\overline{wu} \cong \overline{wv}$ and $m\angle w = 114^\circ$. find $m\angle v$.
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answer attempt 1 out of 2
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Explanation:

Step1: Identify the isosceles triangle property

In an isosceles triangle $\triangle UVW$ with $WU\cong VW$, the base - angles are equal. The sum of angles in a triangle is $180^{\circ}$. Let $\angle V=\angle U = x$.

Step2: Set up the angle - sum equation

We know that $\angle W+\angle V+\angle U = 180^{\circ}$. Since $\angle W = 114^{\circ}$ and $\angle V=\angle U$, we substitute into the equation: $114^{\circ}+x + x=180^{\circ}$.

Step3: Solve the equation for $x$

Combine like terms: $114^{\circ}+2x = 180^{\circ}$. Subtract $114^{\circ}$ from both sides: $2x=180^{\circ}- 114^{\circ}=66^{\circ}$. Divide both sides by 2: $x = 33^{\circ}$.

Answer:

$33^{\circ}$