Question

the figure below is an isosceles triangle.
what is the sum of the angle measures of the isosceles triangle?
180 °
the figure below is an equilateral triangle.
what is the sum of the angle measures of the equilateral triangle?
180 °
what do you notice about the sum of the angle measures?
the sum is 180° for both triangles. the sum is different for different triangles.

Explanation:

To determine the correct option for the question "What do you notice about the sum of the angle measures?", we analyze the angle sums of the two triangles:

• For the isosceles triangle, the angles are \(40^\circ\), \(70^\circ\), and \(70^\circ\). Summing these: \(40^\circ + 70^\circ + 70^\circ = 180^\circ\).
• For the equilateral triangle, the angles are all \(60^\circ\). Summing these: \(60^\circ + 60^\circ + 60^\circ = 180^\circ\).

From this, we observe that the sum of the interior angles of both triangles is \(180^\circ\). This aligns with the triangle angle - sum theorem, which states that the sum of the interior angles of any triangle is always \(180^\circ\), regardless of whether the triangle is isosceles, equilateral, or of any other type.

Answer:

The sum is \(180^\circ\) for both triangles.