A triangle has two 31° angles and one 118° angle. What kind of triangle is it?equilateralisosceles but not equilateralscaleneSubmit
Question
A triangle has two 31° angles and one 118° angle. What kind of triangle is it?
- equilateral
- isosceles but not equilateral
- scalene
Submit
Solution
To determine the type of triangle with angles measuring 31°, 31°, and 118°, we can analyze the characteristics of triangles based on their angles.
1. Break Down the Problem
- Given angles: 31°, 31°, and 118°.
- Identify whether the triangle is equilateral, isosceles, or scalene.
2. Relevant Concepts
- Equilateral Triangle: All three angles are equal (each ).
- Isosceles Triangle: At least two angles are equal.
- Scalene Triangle: All angles are different.
3. Analysis and Detail
- The triangle has two angles of which are equal.
- The third angle is which is different from the other two.
- Since there are two angles that are equal, this confirms that the triangle is isosceles.
4. Verify and Summarize
- The angles add up to , which is the angle sum property for triangles.
- Since it has two equal angles, it categorically fits into the isosceles type and is not equilateral.
Final Answer
The triangle is isosceles but not equilateral.
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