Isosceles triangle has an angle that measures 80°. which other angles could be in that isosceles triangle?-

There are two probabilities of the solution. First if 80° acts as one of the leg angles, second if 80° acts as the vertex angle.

FIRST PROBABILITY
If 80° is one of the leg angles, then the other angle would be 80° too, because iscosceles has two congruent angles on the leg.

Find the vertex angle
the sum of interior angles in a triangle is 180°
vertex angle + angle on the leg + angle on the leg = 180°
vertex angle + 80° + 80° = 180°
vertex angle + 160° = 180°
vertex angle = 180° - 160°
vertex angle = 20°
The interior angles are 80°,80°,20°


SECOND PROBABILITY
If 80° is the vertex angle, we should find the value of the two leg angles. The two legs has congruent angles.

Find the leg angles
the sum of interior angles in a triangle is 180°
leg angle + leg angle + vertex angle = 180°
2 × leg angle + vertex angle = 180°
2 × leg angle + 80° = 180°
2 × leg angle = 180° - 80°
2 × leg angle = 100°
leg angle = 50°
The interior angles are 80°, 50°, 50°