In an isosceles triangle where one of the angles measures 28 degrees, what are the measures of the other two angles? Select all that apply.

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Understanding the Angles of an Isosceles Triangle

In an isosceles triangle, two sides are of equal length, and the angles opposite those sides are also equal. This property is crucial when determining the measures of the angles.

Given Information

We know that one angle is 28 degrees. We will denote the equal angles as θ.

Using the Triangle Angle Sum Theorem

The sum of all angles in a triangle is always 180 degrees. Therefore, we can set up the equation:

28 + θ + θ = 180

Simplifying this, we get:

28 + 2θ = 180

2θ = 180 – 28

2θ = 152

θ = 76 degrees

Possible Angle Measures

Based on our calculations, the other two angles in this isosceles triangle are:

  • 76 degrees (first equal angle)
  • 76 degrees (second equal angle)

Conclusion

So, in summary, the angles of the triangle are:

  • 28 degrees
  • 76 degrees
  • 76 degrees

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