In triangle $ABC$, the measure of angle $A$ is $58°$, and side $a$ is equal to side $c$. What is the measure of angle $C$?

• A. $62°$
• B. $90°$
• C. $64°$
• D. $58°$

Answer: (D)

Verified step by step guidance

1. Identify the given information: In triangle ABC, angle A measures 58\degree, and sides a and c are equal in length.
2. Recall that in a triangle, sides opposite equal angles are equal. Since sides a and c are equal, the angles opposite these sides must also be equal. Therefore, angle B equals angle C.
3. Use the triangle angle sum property, which states that the sum of the interior angles of a triangle is 180\degree. Write the equation: \(A + B + C = 180\degree\).
4. Substitute the known values and relationships into the equation: \$58\degree + B + C = 180\degree\(, and since \)B = C\(, rewrite as \)58\degree + C + C = 180\degree\( or \)58\degree + 2C = 180\degree$.
5. Solve for angle C by isolating it: \$2C = 180\degree - 58\degree\(, then \)C = \frac{180\degree - 58\degree}{2}$. This will give the measure of angle C.