Question

Polygon G H I J K has 5 sides.

Which statements are true about the regular polygon? Select three options.

The sum of the measures of the interior angles is 900°.
Each interior angle measures 108°.
All of the angles are congruent.
The polygon is a regular hexagon.
The sum of the measures of the interior angles is 180(5 – 2)°.

Answer 1

Options B, C, E

Explanation:

Answer 2

• Each interior angle measures 108°.
• All of the angles are congruent.
• The sum of the measures of the interior angles is 180(5 – 2)°.

Explanation:

(1) The sum of the interior angles of a polygon is
`180(n-2)` degrees, where n is the number of sides. In this case, n=5, so the sum is 180(5-2)=540 degrees, meaning the first statement is false.

(2) Since the angles add to 540 degrees, dividing this amongst the five equal angles, we get that each angle measures 108 degrees, so this statement is true.

(3) By definition, all angles of a regular polygon are congruent.

(4) A hexagon has 6 sides, but this polygon has only 5 sides, so this statement is false.

(5) This is true. (See statement (1)).