In the rhombus, m<1 = 18x,
m<2 = x + y, and
m<3 = 30z.
Find the value of the variables x, y, and z.
idk man
To find the values of x, y, and z, we need to use the properties of a rhombus. In a rhombus, opposite angles are congruent, so we can set up equations based on this property.
In the given information, m<1 and m<3 represent opposite angles, so they must be equal. Therefore, we have the equation:
18x = 30z
Similarly, m<2 and m<4 are opposite angles in the rhombus, so they must also be congruent. We can set up another equation using this property:
x + y = 30z
We now have a system of equations:
18x = 30z
x + y = 30z
From these equations, we can try to solve for the variables x, y, and z.
First, let's simplify the first equation by dividing both sides by 6:
3x = 5z
Now, let's substitute this expression for 3x into the second equation:
(3x) + y = 30z
Substituting 5z for 3x:
5z + y = 30z
To isolate y, we need to move the term with y to the other side of the equation:
y = 30z - 5z
Simplifying the right side gives us:
y = 25z
So far, we have found that y = 25z.
Now, let's go back to the first equation:
3x = 5z
To eliminate the fraction, we can multiply both sides by 3:
9x = 15z
Now, let's substitute this expression for 9x into the second equation:
(9x) + y = 30z
Substituting 15z for 9x:
15z + y = 30z
To isolate y, we need to move the term with y to the other side of the equation:
y = 30z - 15z
Simplifying the right side gives us:
y = 15z
Combining this result with the previous result, we have found that y = 15z = 25z.
Now, since y = 25z and y = 15z, we can equate the expressions for y:
25z = 15z
To solve for z, we need to isolate it on one side of the equation. Let's subtract 15z from both sides:
25z - 15z = 15z - 15z
10z = 0
Since any number multiplied by 0 is equal to 0, we have found that z = 0.
Now that we know z = 0, we can substitute this value back into the equation for y:
y = 15z
y = 15(0)
y = 0
Finally, let's substitute z = 0 into the equation for x:
3x = 5z
3x = 5(0)
3x = 0
Again, any number multiplied by 0 is equal to 0, so x = 0.
In conclusion, we have found the values of the variables x, y, and z:
x = 0
y = 0
z = 0