Question

1. in an isosceles triangle, if the base is 8 cm and the base angles are each 60°, what is the length of each of the equal sides? 8 cm 16 cm 12 cm 4 cm

Explanation:

Step1: Recall triangle angle sum property

The sum of angles in a triangle is \(180^\circ\). For an isosceles triangle with base angles \(60^\circ\) each, let the vertex angle be \(x\). So, \(60^\circ + 60^\circ + x = 180^\circ\).

Step2: Calculate the vertex angle

Solving \(120^\circ + x = 180^\circ\), we get \(x = 180^\circ - 120^\circ = 60^\circ\).

Step3: Identify the triangle type

Since all three angles are \(60^\circ\), the triangle is equilateral (all sides equal).

Step4: Determine the equal sides length

The base is \(8\) cm, and in an equilateral triangle, all sides are equal. So each equal side (which are all sides here) is \(8\) cm.

Answer:

8 cm (the option corresponding to 8 cm, e.g., if the first option is "8 cm", then the answer is the first option with its text)