Question

one angle of an isosceles triangle measures 30°, what measures are possible for the other two angles? choose all that apply. 15° 120° 75° 30° submit

Explanation:

Step1: Case 1: 30° is base angle

Let the vertex angle be $x$. Isosceles triangles have 2 equal base angles. Sum of triangle angles is $180^\circ$.
$30^\circ + 30^\circ + x = 180^\circ$
$x = 180^\circ - 60^\circ = 120^\circ$
So other angles: $30^\circ, 120^\circ$

Step2: Case 2: 30° is vertex angle

Let base angles be $y$. Base angles are equal.
$30^\circ + y + y = 180^\circ$
$2y = 180^\circ - 30^\circ = 150^\circ$
$y = \frac{150^\circ}{2} = 75^\circ$
So other angles: $75^\circ, 75^\circ$

Answer:

B. $120^\circ$, C. $75^\circ$, D. $30^\circ$