Question

one angle of an isosceles triangle measures 110°. what measures are possible for the other two angles? choose all that apply. 110° 40° 35° 15°

Explanation:

Step1: Recall triangle - angle sum property

The sum of the interior angles of a triangle is $180^{\circ}$. In an isosceles triangle, two angles are equal.

Step2: Analyze the given angle

The given angle of $110^{\circ}$ cannot be one of the two equal angles because if it were, the sum of those two equal angles ($110^{\circ}+ 110^{\circ}=220^{\circ}$) would already exceed $180^{\circ}$.

Step3: Calculate the equal - angle measure

Let the measure of each of the equal angles be $x$. Then, using the angle - sum property of a triangle, we have $110^{\circ}+x + x=180^{\circ}$. Combining like terms gives $110^{\circ}+2x = 180^{\circ}$. Subtract $110^{\circ}$ from both sides: $2x=180^{\circ}-110^{\circ}=70^{\circ}$. Divide both sides by 2: $x = 35^{\circ}$.

Answer:

C. $35^{\circ}$