Question

note: figure is not drawn to scale. if ab = bc = ca, what is m∠1? a. 60° b. 45° c. 90° d. 180°

Explanation:

Step1: Identify the triangle type

Since \(AB = BC=CA\), \(\triangle ABC\) is an equilateral triangle.

Step2: Recall angle - sum property of equilateral triangle

In an equilateral triangle, all interior angles are equal. Let \(m\angle1 = m\angle2=m\angle3 = x\). The sum of interior angles of a triangle is \(180^{\circ}\), so \(x + x+x=180^{\circ}\).

Step3: Solve for the angle

Combining like - terms gives \(3x = 180^{\circ}\), then \(x=\frac{180^{\circ}}{3}=60^{\circ}\).

Answer:

A. \(60^{\circ}\)