Question

Which of the following statements apply to a regular decagon? i. It has nine congruent sides. ii. It has ten sides. iii. It has a total interior angle measure of 1,800º. iv. It has a total interior angle measure of 1,440º. v. Each interior angle is 144º.

A.
ii, iv, v
B.
ii, iii
C.
ii, v
D.
iv, v

Answer 1

A. ii, iv, v

What is a decagon?

A polygon having ten angles and ten sides.

Answer 2

A. ii, iv, v

Explanation:

You want to know the descriptors that apply to a regular decagon from those on the list ...

• i. 9 congruent sides
• ii. 10 sides
• iii. total angle measure of 1800°
• iv. total angle measure of 1440°
• v. interior angles of 144°

Convex polygon

A convex polygon with n sides has interior angles that total 180°×(n -2). When the number of sides is 10, the total of interior angles is ...

180°×(10 -2) = 1440°

Regular decagon

The prefix "deca-" signifies 10. A regular polygon has congruent sides and angles Thus, a regular decagon has 10 congruent sides and 10 congruent interior angles.

Since the total of interior angles is 1440°, the measure of each is ...

1440°/10 = 144°

Descriptors

The applicable descriptors of the regular decagon are ...

• ii. 10 sides
• iv. total angle measure of 1440°
• v. interior angles of 144°