Question

question 5

1. for every triangle the interior angle sum is...

90°
180°
270°
360°
it varies between acute, right, and obtuse triangles.

Explanation:

Step1: Recall Triangle Angle Sum

The fundamental property of a triangle is that the sum of its interior angles is always a constant. From geometric principles, we know that for any triangle (acute, right, obtuse), the sum of the interior angles is \(180^\circ\). This is a well - known theorem in geometry, and it can also be derived from the polygon angle - sum formula \(180\times(n - 2)\) where \(n = 3\) (for a triangle), so \(180\times(3 - 2)=180^\circ\).

Step2: Eliminate Other Options

• \(90^\circ\) is the measure of a right angle, not the sum of interior angles of a triangle.
• \(270^\circ\) and \(360^\circ\) are angle sums for other polygons (e.g., \(360^\circ\) is the sum of interior angles of a quadrilateral), not a triangle.
• The option "It varies between Acute, Right, and Obtuse Triangles" is incorrect because the sum of interior angles of a triangle is constant and does not vary based on the type of triangle (acute, right, or obtuse).

Answer:

\(180^\circ\) (the option with \(180^\circ\))