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
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
Answers
GPT-4o mini
To determine the true statements about the regular polygon G H I J K, which is a pentagon (5 sides), let's analyze the options provided:
1. **The sum of the measures of the interior angles is 900°**.
This statement is **true**. The formula to calculate the sum of the interior angles of a polygon is:
\[
\text{Sum} = (n - 2) \times 180°
\]
For a pentagon (\(n = 5\)):
\[
\text{Sum} = (5 - 2) \times 180° = 3 \times 180° = 540°
\]
This statement is incorrect as it states 900°.
2. **Each interior angle measures 108°**.
This statement is **true** since for a regular pentagon, the measure of each interior angle can be calculated as:
\[
\text{Each angle} = \frac{\text{Sum of interior angles}}{n} = \frac{540°}{5} = 108°
\]
3. **All of the angles are congruent**.
This statement is **true** because in a regular polygon, all angles are equal (congruent).
4. **The polygon is a regular hexagon**.
This statement is **false** because a hexagon has 6 sides, whereas the polygon in question has 5 sides (it is a pentagon).
5. **The sum of the measures of the interior angles is 180(5)**.
This statement is **false**. The expression \(180(5)\) simplifies to 900°, which is incorrect (as calculated in the first statement).
Therefore, the three true statements are:
- Each interior angle measures 108°.
- All of the angles are congruent.
- The sum of the measures of the interior angles of a pentagon is indeed 540°, not 900°, so this option does not count.
So, your final selections could be:
1. Each interior angle measures 108°.
2. All of the angles are congruent.
You would choose any accurate and relevant statements based on how many must be selected, as options may have discrepancies.
1. **The sum of the measures of the interior angles is 900°**.
This statement is **true**. The formula to calculate the sum of the interior angles of a polygon is:
\[
\text{Sum} = (n - 2) \times 180°
\]
For a pentagon (\(n = 5\)):
\[
\text{Sum} = (5 - 2) \times 180° = 3 \times 180° = 540°
\]
This statement is incorrect as it states 900°.
2. **Each interior angle measures 108°**.
This statement is **true** since for a regular pentagon, the measure of each interior angle can be calculated as:
\[
\text{Each angle} = \frac{\text{Sum of interior angles}}{n} = \frac{540°}{5} = 108°
\]
3. **All of the angles are congruent**.
This statement is **true** because in a regular polygon, all angles are equal (congruent).
4. **The polygon is a regular hexagon**.
This statement is **false** because a hexagon has 6 sides, whereas the polygon in question has 5 sides (it is a pentagon).
5. **The sum of the measures of the interior angles is 180(5)**.
This statement is **false**. The expression \(180(5)\) simplifies to 900°, which is incorrect (as calculated in the first statement).
Therefore, the three true statements are:
- Each interior angle measures 108°.
- All of the angles are congruent.
- The sum of the measures of the interior angles of a pentagon is indeed 540°, not 900°, so this option does not count.
So, your final selections could be:
1. Each interior angle measures 108°.
2. All of the angles are congruent.
You would choose any accurate and relevant statements based on how many must be selected, as options may have discrepancies.