1. How many sides does a regular polygon have if one exterior angle is 90 degrees?
3
4
5
6
2. The measures of three angles of a quadrilateral are 80, 90, and 103 degrees. Find the measure of the fourth angle.
67
77
87
97
3. The sum of the interior angles of a 7-gon is
900
1,080
1,260
1,440
4. One exterior angle of a regular pentagon measures
60
72
90
120
5. If all of the diagonals are drawn from a vertex of a pentagon, how many triangles are formed?
2
3
4
5
6. A polygon is such that when all diagonals from one vertex are drawn, eleven triangles are formed. How many sides does the polygon have?
9
11
12
13
7. The sum of the measures of the interior angles is 1,440 degrees. How many sides does the polygon have?
4
6
8
10
8. How many sides does a regular polygon have if one exterior angle is 1?
120
180
360
1. Ae = 360 / N = 90,
90N = 360,
N = 360 / 90 = 4 Sides.
2. At = 80 + 90 + 103 + x = 360,
X = 360 - 273 = 87 deg.
3. At =(N - 2)180,
At = (7 - 2)180 = 900 deg.
4. Ae = 360 / N = 360 / 5 = 72 DEG.
5.
6.
7. At = (N - 2)180 = 1440,
(N - 2) = 1440 / 180 = 8,
N = 8 - 2 = 6 Sides.
8. Ae = 360 / N = 1 Deg,
N = 360 Sides.
1. To find the number of sides of a regular polygon given an exterior angle, we can use the formula:
Number of sides = 360 degrees / Exterior angle
In this case, if one exterior angle is 90 degrees, we can calculate:
Number of sides = 360 degrees / 90 degrees
Number of sides = 4
Therefore, a regular polygon with one exterior angle measuring 90 degrees has 4 sides.
2. A quadrilateral has four angles whose measures add up to 360 degrees. Given that three of the angles have measures of 80, 90, and 103 degrees, we can find the measure of the fourth angle by subtracting the sum of the known angles from 360 degrees:
360 degrees - (80 degrees + 90 degrees + 103 degrees) = 87 degrees
So, the measure of the fourth angle is 87 degrees.
3. The sum of the interior angles of a polygon can be found using the formula:
Sum of interior angles = (n - 2) * 180 degrees
In this case, we have a 7-gon. Plugging the value of n into the formula:
Sum of interior angles = (7 - 2) * 180 degrees
Sum of interior angles = 5 * 180 degrees
Sum of interior angles = 900 degrees
Therefore, the sum of the interior angles of a 7-gon is 900 degrees.
4. The measure of each exterior angle of a regular polygon can be found using the formula:
Measure of each exterior angle = 360 degrees / Number of sides
In the case of a regular pentagon, the number of sides is 5, so:
Measure of each exterior angle = 360 degrees / 5
Measure of each exterior angle = 72 degrees
Therefore, one exterior angle of a regular pentagon measures 72 degrees.
5. To find the number of triangles formed by drawing diagonals from a vertex of a polygon, we use the formula:
Number of triangles = Number of sides - 2
In the case of a pentagon, which has 5 sides:
Number of triangles = 5 - 2
Number of triangles = 3
So, if all diagonals are drawn from a vertex of a pentagon, three triangles are formed.
6. If all diagonals drawn from one vertex of a polygon form eleven triangles, we can use the formula:
Number of sides = Number of triangles + 2
In this case, if eleven triangles are formed:
Number of sides = 11 + 2
Number of sides = 13
Therefore, the polygon has 13 sides.
7. The sum of the measures of the interior angles of a polygon can be found using the formula:
Sum of interior angles = (n - 2) * 180 degrees
Given that the sum is 1,440 degrees, we can solve for n:
1,440 degrees = (n - 2) * 180 degrees
n - 2 = 1,440 degrees / 180 degrees
n - 2 = 8
n = 8 + 2
n = 10
Therefore, the polygon has 10 sides.
8. If one exterior angle of a regular polygon measures 1 degree, we can find the number of sides using the formula:
Number of sides = 360 degrees / Exterior angle
In this case:
Number of sides = 360 degrees / 1 degree
Number of sides = 360
Therefore, a regular polygon with one exterior angle measuring 1 degree has 360 sides.
1. If one exterior angle of a regular polygon is 90 degrees, then the polygon has 4 sides.
2. To find the measure of the fourth angle of a quadrilateral, we can subtract the sum of the given angles from 360 degrees.
360 - (80 + 90 + 103) = 87 degrees.
3. The sum of the interior angles of a polygon can be found using the formula (n-2) * 180, where n is the number of sides of the polygon.
For a 7-gon, the sum of the interior angles = (7-2) * 180 = 5 * 180 = 900 degrees.
4. The formula for finding the measure of an exterior angle of a regular polygon is 360 / n, where n is the number of sides of the polygon.
For a regular pentagon, the measure of an exterior angle = 360 / 5 = 72 degrees.
5. If all diagonals are drawn from a vertex of a pentagon, 5 triangles are formed.
6. If all diagonals from one vertex of a polygon form 11 triangles, we can use the formula (n-2) * (n-3) / 2. We can solve for n by setting the equation equal to 11 and solving for n.
(n-2) * (n-3) / 2 = 11
Simplifying this equation will give us n = 13.
7. The sum of the measures of the interior angles of a polygon can be found using the formula (n-2) * 180, where n is the number of sides of the polygon.
If the sum of the interior angles is 1,440 degrees, then we can set up the equation (n-2) * 180 = 1,440.
Simplifying this equation will give us n = 10.
8. If one exterior angle of a regular polygon is 1 degree, we can use the formula 360 / n to find the number of sides of the polygon.
360 / 1 = 360 sides.