Question
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Question
Use the image to answer the question.
An illustration shows a triangle in which the two opposite sides are of same length, as indicated by congruent cross marks on each side. The angle formed by the convergence of these sides of the same length is 18 degrees. The two angles of the base opposite to the 18 degrees vertex are each labeled as x.
Find the value of x
.
(1 point)
Responses
81°
81 degrees
76°
76 degrees
162°
162 degrees
80°
80 degrees
1 of 121 of 12 Items
Question
Use the image to answer the question.
An illustration shows a triangle in which the two opposite sides are of same length, as indicated by congruent cross marks on each side. The angle formed by the convergence of these sides of the same length is 18 degrees. The two angles of the base opposite to the 18 degrees vertex are each labeled as x.
Find the value of x
.
(1 point)
Responses
81°
81 degrees
76°
76 degrees
162°
162 degrees
80°
80 degrees
Answers
GPT-4o mini
In this triangle, we have an isosceles triangle where the two sides are of equal length, which corresponds with the two angles (labeled as \( x \)) opposite to those sides being equal.
In any triangle, the sum of the interior angles equals 180 degrees. Here, we can set up the equation based on the known angles:
\[
x + x + 18° = 180°
\]
This simplifies to:
\[
2x + 18° = 180°
\]
Subtracting 18° from both sides gives:
\[
2x = 162°
\]
Dividing both sides by 2 results in:
\[
x = 81°
\]
Therefore, the value of \( x \) is \( 81° \).
So the correct response is:
**81°**
In any triangle, the sum of the interior angles equals 180 degrees. Here, we can set up the equation based on the known angles:
\[
x + x + 18° = 180°
\]
This simplifies to:
\[
2x + 18° = 180°
\]
Subtracting 18° from both sides gives:
\[
2x = 162°
\]
Dividing both sides by 2 results in:
\[
x = 81°
\]
Therefore, the value of \( x \) is \( 81° \).
So the correct response is:
**81°**