Given that an equilateral triangle and an isosceles triangle share a common side, and the triangle $ABC$ is equilateral, what is the measure of angle $\angle ABC$ in degrees?

• A. $90$
• B. $120$
• C. $45$
• D. $60$

Answer: (D)

Verified step by step guidance

1. Recall the definition of an equilateral triangle: all three sides are equal in length, and all three interior angles are equal.
2. Since triangle ABC is equilateral, each interior angle must be the same. The sum of interior angles in any triangle is 180 degrees.
3. Divide the total sum of angles (180 degrees) by the number of angles (3) to find the measure of each angle in the equilateral triangle.
4. Express this calculation as: \(\frac{180}{3}\) degrees, which gives the measure of angle \(\angle ABC\).
5. Conclude that the measure of angle \(\angle ABC\) in the equilateral triangle is 60 degrees.