Question

an isosceles triangle has an angle that measures 30°. what measures are possible for the other two angles? choose all that apply. 30° 20° 120° 75°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In an isosceles triangle, two angles are equal.

Step2: Case 1: The 30° angle is one of the equal angles

Let the equal angles be 30° each. Then the third angle is $180-(30 + 30)=120°$.

Step3: Case 2: The 30° angle is not one of the equal angles

Let the equal angles be $x$ each. Then $30+2x = 180$. Solving for $x$, we get $2x=180 - 30=150$, so $x = 75°$.

Answer:

30°, 120°, 75°