What is the sum of the measures of the angles of this 9-sided polygon?
1,080
1.260
1.440
1.620

1.260

Step-by-step 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)

ShapeSidesSum of

Interior AnglesShapeEach Angle

Triangle3180°regular triangle60°

Quadrilateral4360°regular quadrilateral90°

Pentagon5540°pentagon regular108°

Hexagon6720°hexagon regular120°

Heptagon (or Septagon)7900°heptagon refular128.57...°

Octagon81080°octagon regular135°

Nonagon91260°nonagon regular140°

Any Polygonn(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"

5/12, or 5: 12

step-by-step explanation:

the answer is 99.