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: Caso 1: 80° es ángulo base

La suma de ángulos de triángulo es $180^\circ$. Los dos ángulos base son iguales. Sea $x$ el ángulo vértice:
$$x + 80^\circ + 80^\circ = 180^\circ$$
$$x = 180^\circ - 160^\circ = 20^\circ$$

Step2: Caso 2: 80° es ángulo vértice

Sea $y$ cada ángulo base (iguales):
$$80^\circ + 2y = 180^\circ$$
$$2y = 180^\circ - 80^\circ = 100^\circ$$
$$y = \frac{100^\circ}{2} = 50^\circ$$

Answer:

• 50°
• 20°
• 80°