Question
The vertex angle of an isosceles triangle is 110 degrees. What are the measures of the base angles?
ListenResponse
30 and 40 degrees.
ListenResponse
35 and 35 degrees.
ListenResponse
55 and 55 degrees.
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60 and 10 degrees.
ListenResponse
30 and 40 degrees.
ListenResponse
35 and 35 degrees.
ListenResponse
55 and 55 degrees.
ListenResponse
60 and 10 degrees.
Answers
GPT-4o mini
In an isosceles triangle, the two base angles are equal, and the sum of all three angles in a triangle is always 180 degrees.
Given that the vertex angle is 110 degrees, we can find the measures of the base angles as follows:
1. Calculate the sum of the base angles:
\[
\text{Sum of base angles} = 180^\circ - \text{vertex angle} = 180^\circ - 110^\circ = 70^\circ.
\]
2. Since the base angles are equal, we divide this sum by 2:
\[
\text{Each base angle} = \frac{70^\circ}{2} = 35^\circ.
\]
Thus, the measures of the base angles are 35 degrees each.
The correct answer is **35 and 35 degrees**.
Given that the vertex angle is 110 degrees, we can find the measures of the base angles as follows:
1. Calculate the sum of the base angles:
\[
\text{Sum of base angles} = 180^\circ - \text{vertex angle} = 180^\circ - 110^\circ = 70^\circ.
\]
2. Since the base angles are equal, we divide this sum by 2:
\[
\text{Each base angle} = \frac{70^\circ}{2} = 35^\circ.
\]
Thus, the measures of the base angles are 35 degrees each.
The correct answer is **35 and 35 degrees**.