Question

What is the sum of the measures of the angles of this 9-sided polygon?

1,080
1.260
1.440
1.620​

Answer 1

1.260

Explanation:

Each time we add a side (triangle to quadrilateral, quadrilateral to pentagon, etc), we add another 180° to the total:

If it is a Regular Polygon (all sides are equal, all angles are equal)

Shape Sides Sum of

Interior Angles Shape Each Angle

Triangle 3 180° regular triangle 60°

Quadrilateral 4 360° regular quadrilateral 90°

Pentagon 5 540° pentagon regular 108°

Hexagon 6 720° hexagon regular 120°

Heptagon (or Septagon) 7 900° heptagon refular 128.57...°

Octagon 8 1080° octagon regular 135°

Nonagon 9 1260° nonagon regular 140°

Any Polygon n (n−2) × 180° regular n gon (n−2) × 180° / n

So the general rule is:

Sum of Interior Angles = (n−2) × 180°

Each Angle (of a Regular Polygon) = (n−2) × 180° / n

Perhaps an example will help:

Example: What about a Regular Decagon (10 sides) ?

regular decagon

Sum of Interior Angles = (n−2) × 180°

= (10−2) × 180°

= 8 × 180°

= 1440°

And for a Regular Decagon:

Each interior angle = 1440°/10 = 144°

Note: Interior Angles are sometimes called "Internal Angles"

Answer 2

The answer would be B. 1.260