the base angle of an isosceles triangle measures ( 54^{circ} ). what is the measure of its vertex angle?

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Accepted Answer

# Explanation:
## Step1: Recall the property of isosceles triangle
In an isosceles triangle, the two base angles are equal. Let the base angles be $B_1 = B_2=54^{\circ}$.
## Step2: Use the angle - sum property of a triangle
The sum of the interior angles of a triangle is $180^{\circ}$. Let the vertex angle be $V$. Then $V + B_1 + B_2=180^{\circ}$.
Substitute $B_1 = B_2 = 54^{\circ}$ into the equation: $V+54^{\circ}+54^{\circ}=180^{\circ}$.
## Step3: Solve for the vertex angle $V$
$$
\begin{align*}
V&=180^{\circ}-(54^{\circ}+54^{\circ})\
V&=180^{\circ}-108^{\circ}\
V& = 72^{\circ}
\end{align*}
$$

# Answer:
$72^{\circ}$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the property of isosceles triangle

Step2: Use the angle - sum property of a triangle

Step3: Solve for the vertex angle \(V\)

Answer: