Question
The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle?
27°
36°
54°
72°
27°
36°
54°
72°
Answers
GPT-4o mini
In an isosceles triangle, the two base angles are equal. If the base angle measures \(54^\circ\), then the other base angle is also \(54^\circ\).
To find the vertex angle, we use the fact that the sum of all angles in a triangle is \(180^\circ\).
Let \(x\) be the measure of the vertex angle. The equation can be set up as follows:
\[
54^\circ + 54^\circ + x = 180^\circ
\]
Simplifying the left side:
\[
108^\circ + x = 180^\circ
\]
Now, subtract \(108^\circ\) from both sides:
\[
x = 180^\circ - 108^\circ
\]
Calculating the result:
\[
x = 72^\circ
\]
Therefore, the measure of the vertex angle is \(72^\circ\).
The answer is \(72^\circ\).
To find the vertex angle, we use the fact that the sum of all angles in a triangle is \(180^\circ\).
Let \(x\) be the measure of the vertex angle. The equation can be set up as follows:
\[
54^\circ + 54^\circ + x = 180^\circ
\]
Simplifying the left side:
\[
108^\circ + x = 180^\circ
\]
Now, subtract \(108^\circ\) from both sides:
\[
x = 180^\circ - 108^\circ
\]
Calculating the result:
\[
x = 72^\circ
\]
Therefore, the measure of the vertex angle is \(72^\circ\).
The answer is \(72^\circ\).