Question

question 1: explore polygon interior angle sums what is the interior angle sum for a convex octagon? question 6 6. in the formula (n - 2)·180° = the sum of the interior angles of a polygon with n sides. what does the n - 2 stand for? options: the number of sides of a polygon; the number of angles of a regular polygon; the number of non - overlapping triangles that can be drawn in the interior of the polygon; the number of interior angles you want to add together.

Explanation:

Question 1:

Step1: Recall the formula for the sum of interior angles of a polygon.

The formula for the sum of the interior angles of a polygon with \( n \) sides is \( (n - 2)\times180^{\circ} \).

Step2: Identify the number of sides of an octagon.

An octagon has \( n = 8 \) sides.

Step3: Substitute \( n = 8 \) into the formula.

Substitute \( n = 8 \) into \( (n - 2)\times180^{\circ} \), we get \( (8 - 2)\times180^{\circ} \).

Step4: Calculate the value.

First, calculate \( 8 - 2 = 6 \), then \( 6\times180^{\circ}=1080^{\circ} \).

• The first option: The number of sides of a polygon is \( n \), not \( n - 2 \), so this is incorrect.
• The second option: The number of angles of a regular polygon is equal to the number of sides \( n \), not \( n - 2 \), so this is incorrect.
• The third option: When we draw non - overlapping triangles inside a polygon from one vertex, the number of such triangles is \( n - 2 \). And since the sum of interior angles of a triangle is \( 180^{\circ} \), we multiply \( (n - 2) \) by \( 180^{\circ} \) to get the sum of interior angles of the polygon. So this option is correct.
• The fourth option: \( n - 2 \) has nothing to do with the number of interior angles we want to add together in this context, so this is incorrect.

Answer:

The interior angle sum for a convex octagon is \( 1080^{\circ} \).

Question 6: