If the vertex angle of an isosceles triangle is $110°$, what is the measure of each base angle?

• A. $55°$
• B. $70°$
• C. $45°$
• D. $35°$

Answer: (D)

Verified step by step guidance

1. Recall that the sum of the interior angles of any triangle is always \$180^\circ$.
2. Identify the given angle: the vertex angle of the isosceles triangle is \$110^\circ$.
3. Since the triangle is isosceles, the two base angles are equal. Let each base angle be \(x\) degrees.
4. Set up the equation for the sum of angles: \$110^\circ + x + x = 180^\circ$.
5. Solve for \(x\): combine like terms to get \$110^\circ + 2x = 180^\circ\(, then subtract \)110^\circ\( from both sides to find \)2x = 70^\circ\(, and finally divide both sides by 2 to get \)x = 35^\circ$.