Final answer:
An isosceles triangle with one 32° angle could either have two 74° angles if the 32° is the vertex angle, or it could have another 32° angle and one 116° angle if the 32° angle is one of the base angles.
Step-by-step explanation:
When dealing with an isosceles triangle, you must remember that it has two sides of equal length, and the angles opposite those sides are also equal. Since the sum of the angles in any triangle is always 180 degrees, and one of the angles is given as 32°, there are two cases to consider for an isosceles triangle with a 32° angle:
If the 32° angle is the vertex angle (the angle between the two equal sides), then the base angles must also be equal and add up to 180° - 32° = 148°. Therefore, each base angle would be 148° / 2 = 74°.
If the 32° angle is one of the base angles, then the other base angle is also 32°, and the vertex angle would be 180° - 32° - 32° = 116°.
In summary, an isosceles triangle with one angle measuring 32° could have the other two angles as either two 74° angles or one 32° angle and one 116° angle.