Question
The image shows a triangle with two equal sides measuring 12 units and a base measuring 10.4 units, making it an isosceles triangle. The angle between the two equal sides is labeled as 62°, and the angle opposite the base is labeled as x, which is one of the two congruent base angles. The question asks for the value of x in this triangle.
find the value of x in the triangle described above
find the value of x in the triangle described above
Answers
GPT-4o mini
To find the value of the angle \( x \) in the isosceles triangle, we can use the property that the sum of the angles in any triangle is \( 180^\circ \).
In the given triangle, we know:
- The vertex angle (the angle between the two equal sides) is \( 62^\circ \).
- The base angles are equal, and we can label each base angle as \( x \).
The sum of the angles in the triangle can be expressed as:
\[
62^\circ + x + x = 180^\circ
\]
This simplifies to:
\[
62^\circ + 2x = 180^\circ
\]
Now, we can isolate \( 2x \):
\[
2x = 180^\circ - 62^\circ
\]
\[
2x = 118^\circ
\]
Next, we divide by 2 to find \( x \):
\[
x = \frac{118^\circ}{2} = 59^\circ
\]
Thus, the value of \( x \) is \( \boxed{59^\circ} \).
In the given triangle, we know:
- The vertex angle (the angle between the two equal sides) is \( 62^\circ \).
- The base angles are equal, and we can label each base angle as \( x \).
The sum of the angles in the triangle can be expressed as:
\[
62^\circ + x + x = 180^\circ
\]
This simplifies to:
\[
62^\circ + 2x = 180^\circ
\]
Now, we can isolate \( 2x \):
\[
2x = 180^\circ - 62^\circ
\]
\[
2x = 118^\circ
\]
Next, we divide by 2 to find \( x \):
\[
x = \frac{118^\circ}{2} = 59^\circ
\]
Thus, the value of \( x \) is \( \boxed{59^\circ} \).