Question

3.fill in the blanks:
the interior angle sum theorem states that angles inside a triangle add up to ____°.
the exterior angle theorem states that an exterior angle equals the sum of the two __ __ angles.

Explanation:

First Blank

Step1: Recall the interior angle sum theorem for triangles

By the interior angle sum theorem of a triangle, the sum of the interior angles of a triangle is a well - known constant.
Let the three interior angles of a triangle be \(A\), \(B\), and \(C\). We can prove this using parallel line properties (e.g., draw a line parallel to one side of the triangle through the opposite vertex and use alternate interior angles). The sum \(A + B+C=180^{\circ}\).

Second Blank

Step1: Recall the exterior angle theorem

Let \(\angle ACD\) be an exterior angle of \(\triangle ABC\) (where \(D\) is a point on the extension of \(BC\)).
By the exterior angle theorem, \(\angle ACD=\angle A+\angle B\). Here, \(\angle A\) and \(\angle B\) are the non - adjacent (or remote) interior angles with respect to the exterior angle \(\angle ACD\).

Answer:

1. \(180^{\circ}\)
2. non - adjacent (or remote) interior