Question

one angle of an isosceles triangle measures 40°. what measures are possible for the other two angles? choose all that apply. 40° 70° 20° 100°

Explanation:

Step1: Recall triangle angle sum

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

Step2: Case1: 40° is a base angle

Let the vertex angle be $x$. Since base angles are equal:
$40^\circ + 40^\circ + x = 180^\circ$
$x = 180^\circ - 80^\circ = 100^\circ$
So other angles: $40^\circ, 100^\circ$

Step3: Case2: 40° is the vertex angle

Let base angles be $y$. Base angles are equal:
$40^\circ + y + y = 180^\circ$
$2y = 180^\circ - 40^\circ = 140^\circ$
$y = \frac{140^\circ}{2} = 70^\circ$
So other angles: $70^\circ, 70^\circ$

Step4: Identify valid angles

Possible other angles are $40^\circ, 70^\circ, 100^\circ$.

Answer:

40°, 70°, 100°