Question

one angle of an isosceles triangle measures 80°. what measures are possible for the other two angles? choose all that apply. 80° 50° 20° 10°

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is $180^\circ$.

Step2: Case 1: 80° is a base angle

Isosceles triangles have 2 equal base angles. Let the third angle be $x$.
$x + 80^\circ + 80^\circ = 180^\circ$
$x = 180^\circ - 160^\circ = 20^\circ$

Step3: Case 2: 80° is the vertex angle

Let each base angle be $y$.
$80^\circ + 2y = 180^\circ$
$2y = 180^\circ - 80^\circ = 100^\circ$
$y = \frac{100^\circ}{2} = 50^\circ$

Answer:

80°, 50°, 20°