1. An exterior angle of a regular polygon measures 30 degrees. What is the measure of an interior angle?
30
60
120
150
2. How many degrees are in each interior angle of a regular pentagon?
50
72
108
120
3. If all of the diagonals are drawn from a vertex of a hexagon, how many triangles are formed?
2
3
4
5
4. Find the number of sides of a regular polygon if one interior angle is 120 degrees.
3
4
5
6
5. If all of the diagonals are drawn from a vertex of an octagon, how many triangles are formed?
5
6
7
8
6. Find the number of sides of a regular polygon if one interior angle is 60 degrees.
3
4
5
6
7. If all of the diagonals are drawn from a vertex of a quadrilateral, how many triangles are formed?
1
2
3
4
8. If all of the diagonals are drawn from a vertex of an n-gon, how many triangles are formed?
n - 2
n - 1
n
n + 1
9. What is the measure of one exterior angle of a regular hexagon?
60
72
for question 3. i got 4
1. To find the measure of an interior angle of a regular polygon, we can use the formula:
Interior angle = (180 - Exterior angle)
In this case, the exterior angle measures 30 degrees. Therefore, the interior angle would be:
Interior angle = (180 - 30) = 150 degrees
So, the measure of the interior angle is 150 degrees. (Option D)
2. To find the measure of each interior angle of a regular pentagon, we can use the formula:
Interior angle = (180 * (n - 2)) / n
In this case, n = 5 (since it is a pentagon). Substituting this value in the formula, we get:
Interior angle = (180 * (5 - 2)) / 5
Interior angle = (180 * 3) / 5
Interior angle = 540 / 5
Interior angle = 108 degrees
So, each interior angle of a regular pentagon measures 108 degrees. (Option C)
3. When all the diagonals are drawn from a vertex of a hexagon, we form 4 triangles. (Option C)
4. To find the number of sides of a regular polygon, given the measure of an interior angle, we can use the formula:
Number of sides = 360 / Interior angle
In this case, the measure of the interior angle is 120 degrees. Therefore, the number of sides would be:
Number of sides = 360 / 120 = 3
So, the number of sides of a regular polygon with an interior angle of 120 degrees is 3. (Option A)
5. When all the diagonals are drawn from a vertex of an octagon, we form 6 triangles. (Option B)
6. To find the number of sides of a regular polygon, given the measure of an interior angle, we can use the formula:
Number of sides = 360 / Interior angle
In this case, the measure of the interior angle is 60 degrees. Therefore, the number of sides would be:
Number of sides = 360 / 60 = 6
So, the number of sides of a regular polygon with an interior angle of 60 degrees is 6. (Option D)
7. When all the diagonals are drawn from a vertex of a quadrilateral (4-sided polygon), we form 2 triangles. (Option B)
8. When all the diagonals are drawn from a vertex of an n-gon, we form (n - 2) triangles. (Option A)
9. The measure of one exterior angle of a regular hexagon can be found using the formula:
Exterior angle = 360 / Number of sides
In this case, the number of sides is 6 (since it is a hexagon). Substituting this value in the formula, we get:
Exterior angle = 360 / 6 = 60 degrees
So, the measure of one exterior angle of a regular hexagon is 60 degrees. (Option A)
To find the measure of an interior angle of a regular polygon, we use the formula:
Interior angle = (n-2) * 180° / n
where n is the number of sides of the polygon.
For question 1, if the exterior angle measures 30 degrees, then the interior angle would be:
Interior angle = (180° - 30°) = 150°
So, the answer is 150 degrees.
For question 2, we need to find the number of degrees in each interior angle of a regular pentagon. By using the formula mentioned above, we get:
Interior angle = (5-2) * 180° / 5 = 108°
So, the answer is 108 degrees.
For question 3, if all the diagonals are drawn from a vertex of a hexagon, six triangles are formed.
So, the answer is 6.
For question 4, we know that one interior angle is 120 degrees. Using the formula mentioned earlier:
120 = (n-2) * 180° / n
Simplifying this equation, we can find the value of n:
120n = 180n - 360
60n = 360
n = 6
So, the answer is 6 sides.
For question 5, if all the diagonals are drawn from a vertex of an octagon, five triangles are formed.
So, the answer is 5.
For question 6, we know that one interior angle is 60 degrees. Using the formula mentioned earlier:
60 = (n-2) * 180° / n
Simplifying this equation, we can find the value of n:
60n = 180n - 360
120n = 360
n = 3
So, the answer is 3 sides.
For question 7, if all the diagonals are drawn from a vertex of a quadrilateral, two triangles are formed.
So, the answer is 2.
For question 8, if all the diagonals are drawn from a vertex of an n-gon, the number of triangles formed is (n-2).
So, the answer is (n-2).
For question 9, the measure of one exterior angle of a regular hexagon is calculated using the formula:
Exterior angle = 360° / n
where n is the number of sides of the polygon.
So, the answer is 360° / 6 = 60 degrees.
Did you just expect somebody to give you all those answers?
Tell me what you get for each of them and I will correct them for you.