Question
How many triangles can be constructed with two angles measuring 80∘ and 100° ?
Question 2 options:
zero
one
more than one
Question 2 options:
zero
one
more than one
Answers
GPT-4o mini
To determine how many triangles can be constructed with two angles measuring \(80^\circ\) and \(100^\circ\), we first need to check if a triangle can exist with these angle measures.
The sum of the angles in a triangle must always equal \(180^\circ\). Let's calculate the sum of the given angles:
\[
80^\circ + 100^\circ = 180^\circ
\]
Since the sum of the two angles equals \(180^\circ\), this means that the third angle would need to measure \(0^\circ\) (since \(180^\circ - 80^\circ - 100^\circ = 0^\circ\)).
However, a triangle cannot have an angle of \(0^\circ\), as that would not form a closed figure. Therefore, a triangle cannot be formed with these angle measures.
Thus, the answer is:
**zero**
The sum of the angles in a triangle must always equal \(180^\circ\). Let's calculate the sum of the given angles:
\[
80^\circ + 100^\circ = 180^\circ
\]
Since the sum of the two angles equals \(180^\circ\), this means that the third angle would need to measure \(0^\circ\) (since \(180^\circ - 80^\circ - 100^\circ = 0^\circ\)).
However, a triangle cannot have an angle of \(0^\circ\), as that would not form a closed figure. Therefore, a triangle cannot be formed with these angle measures.
Thus, the answer is:
**zero**