In a parallelogram, opposite sides are equal in length. Since LMNO is a parallelogram, we can set up the following equation:
ON = LM
8x - 8 = 7x + 4
x = 12
We also know that NO = LM
NM = LM
x - 5 = 7x + 4
6x = -9
x = -3/2
Therefore, x = 12 and x = -3/2, which means LMNO must be a parallelogram.
Now, let's find the value of y.
OL = NM
3y - 6 = x - 5
3y - 6 = (-3/2) - 5
3y = -17/2
y = -17/6
Therefore, the values of x and y for which LMNO must be a parallelogram are x = 12 and y = -17/6.
If ON=8x–8, LM=7x+4, NM=x–5, and OL=3y–6, find the values of x and y for which LMNO must be a parallelogram. The diagram is not drawn to scale.
11 answers
In parallelogram DEFG, DH = x + 1, HF = 3y, GH = 3x – 4, and HE = 5y + 1. Find the values of x and y. The diagram is not drawn to scale.
In a parallelogram, opposite sides are equal in length. Since DEFG is a parallelogram, we can set up the following equations:
DH = GH
x + 1 = 3x - 4
Solving this equation, we get:
2x = 5
x = 5/2
HF = HE
3y = 5y + 1
Solving this equation, we get:
-2y = 1
y = -1/2
Therefore, the values of x and y for which DEFG must be a parallelogram are x = 5/2 and y = -1/2.
DH = GH
x + 1 = 3x - 4
Solving this equation, we get:
2x = 5
x = 5/2
HF = HE
3y = 5y + 1
Solving this equation, we get:
-2y = 1
y = -1/2
Therefore, the values of x and y for which DEFG must be a parallelogram are x = 5/2 and y = -1/2.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. How many sides does a regular polygon have if each exterior angle measures 72° ?
Let's denote the number of sides of the regular polygon as n.
In a regular polygon, the sum of all exterior angles is always 360°.
Since each exterior angle measures 72°, we can set up the following equation:
72n = 360
To solve for n, we divide both sides of the equation by 72:
n = 360/72
n = 5
Therefore, a regular polygon with each exterior angle measuring 72° has 5 sides.
In a regular polygon, the sum of all exterior angles is always 360°.
Since each exterior angle measures 72°, we can set up the following equation:
72n = 360
To solve for n, we divide both sides of the equation by 72:
n = 360/72
n = 5
Therefore, a regular polygon with each exterior angle measuring 72° has 5 sides.
The sum of the measures of two exterior angles of a triangle is 264° . What is the measure of the third exterior angle?
The sum of the measures of all exterior angles of any polygon, including a triangle, is always 360°.
Let's denote the measures of the two given exterior angles as x and y.
We know that x + y = 264°, which represents the sum of these two angles.
To find the measure of the third exterior angle, we can subtract the sum of the measures of the two given exterior angles from 360°:
360° - (x + y) = third exterior angle
Simplifying this equation, we get:
360° - 264° = third exterior angle
96° = third exterior angle
Therefore, the measure of the third exterior angle is 96°.
Let's denote the measures of the two given exterior angles as x and y.
We know that x + y = 264°, which represents the sum of these two angles.
To find the measure of the third exterior angle, we can subtract the sum of the measures of the two given exterior angles from 360°:
360° - (x + y) = third exterior angle
Simplifying this equation, we get:
360° - 264° = third exterior angle
96° = third exterior angle
Therefore, the measure of the third exterior angle is 96°.
The sum of the angle measures of a polygon with s sides is 2,340° . Find s.
To find the number of sides, denoted as s, we can use the formula for the sum of the interior angles of a polygon:
Sum of interior angles = (s-2) * 180°
In this case, we are given that the sum of the interior angles is 2,340°.
Therefore, we can set up the following equation:
(s-2)*180° = 2,340°
Dividing both sides by 180°, we get:
s - 2 = 13
Adding 2 to both sides, we have:
s = 15
Therefore, the polygon has 15 sides.
Sum of interior angles = (s-2) * 180°
In this case, we are given that the sum of the interior angles is 2,340°.
Therefore, we can set up the following equation:
(s-2)*180° = 2,340°
Dividing both sides by 180°, we get:
s - 2 = 13
Adding 2 to both sides, we have:
s = 15
Therefore, the polygon has 15 sides.
Find the sum of the measures of the interior angles of the figure. the figure is a regular hexagon, show the work to find this answer.
A regular hexagon has 6 sides. To find the sum of the measures of its interior angles, we can use the formula:
Sum of interior angles = (s-2) * 180°
In this case, the number of sides, s, is 6.
Therefore, the sum of the measures of the interior angles of a regular hexagon is:
(6-2) * 180° = 4 * 180° = 720°
So, the sum of the measures of the interior angles of a regular hexagon is 720°.
Sum of interior angles = (s-2) * 180°
In this case, the number of sides, s, is 6.
Therefore, the sum of the measures of the interior angles of a regular hexagon is:
(6-2) * 180° = 4 * 180° = 720°
So, the sum of the measures of the interior angles of a regular hexagon is 720°.