consider an isosceles triangle with one angle measuring 30 degrees.

Question

what could be the measures of the other two angles, in degrees, of this triangle

Answer 1

In an isosceles triangle, two angles are equal. If one angle of the triangle measures 30 degrees, we can consider two scenarios:

1. The angle measuring 30 degrees is one of the equal angles.

   • In this case, let the equal angles be \( x \). Therefore, you have: \[ x + x + 30 = 180 \] Simplifying this, we get: \[ 2x + 30 = 180 \] \[ 2x = 180 - 30 \] \[ 2x = 150 \] \[ x = 75 \] Thus, the measures of the angles would be 30 degrees, 75 degrees, and 75 degrees.

2. The angle measuring 30 degrees is the unique angle.

   • In this scenario, the two equal angles would still be represented as \( x \). You would set up the equation as follows: \[ x + x + 30 = 180 \] Which simplifies to the same equation as above: \[ 2x + 30 = 180 \] Following the same steps, we find the equal angles would again measure 75 degrees.

In either case, the measures of the angles in the isosceles triangle are 30 degrees, 75 degrees, and 75 degrees.