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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

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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 6060^\circ).
  • Isosceles Triangle: At least two angles are equal.
  • Scalene Triangle: All angles are different.

3. Analysis and Detail

  • The triangle has two angles of 3131^\circ which are equal.
  • The third angle is 118118^\circ 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 31+31+118=18031 + 31 + 118 = 180^\circ, 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.

This problem has been solved

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