Given an isosceles triangle $ABC$ with angle $B$ equal to $130°$, what is the measure of each of the other two angles?

• A. $25°$ and $25°$
• B. $40°$ and $10°$
• C. $50°$ and $50°$
• D. $130°$ and $20°$

Answer: (A)

Verified step by step guidance

1. Recall that the sum of the interior angles in any triangle is always \$180^\circ$. This is a fundamental property of triangles.
2. Since triangle ABC is isosceles, it has two equal sides and therefore two equal angles. Identify which angles are equal. Given that angle \(B\) is \$130^\circ\(, the other two angles, \)A\( and \)C$, must be equal.
3. Set the measure of each of the equal angles as \(x\). Then write the equation for the sum of the angles: \$130^\circ + x + x = 180^\circ$.
4. Simplify the equation to \$130^\circ + 2x = 180^\circ\( and then isolate \)x\( by subtracting \)130^\circ\( from both sides: \)2x = 180^\circ - 130^\circ$.
5. Finally, solve for \(x\) by dividing both sides by 2: \(x = \frac{180^\circ - 130^\circ}{2}\). This will give you the measure of each of the other two equal angles.