A. Find the values of a and b that would make the quadrilateral a parallelogram.
B. Make sure to show work
Top 6b-3
Left 2a+6
Right 3a-10
Bottom 5a+1
Thank you
In a ||gram, opposite sides are equal, so
6b-3 = 5a + 1
5a - 6b = -4
and
2a + 6 = 3a-10
a = 16
into the first:
5(16) - 6b = -4
-6b = -84
b = 14
check:
top = 6b-3 = 81
left = 2a + 6 = 38
right = 3a - 10 = 38
bottom = 5a+1 = 81
all is good!
My parallelogram has top right angle of (12b+8)degrees, bottom right angle of (5b+2) degrees, and a bottom left angle of 2a degrees please help me solve for a and b.
A. To determine the values of a and b that would make the quadrilateral a parallelogram, we need to set the opposite sides equal to each other.
Top: 6b - 3
Bottom: 5a + 1
Since a parallelogram has opposite sides that are equal, we can set these expressions equal to each other:
6b - 3 = 5a + 1
B. Now, let's solve for a and b by simplifying and isolating variables.
6b = 5a + 1 + 3
6b = 5a + 4
Divide both sides by 6:
b = (5a + 4) / 6
And that, ladies and gentlemen, is the value of b in terms of a for a parallelogram. If you want a specific numerical value for b, you'll need to provide a value for a. Now that's a solved riddle!
Disclaimer: All jokes aside, remember to show your work thoroughly and demonstrate your problem-solving skills in a clear manner. Not all problems can be solved using humor, but it sure makes math more fun!
To determine the values of a and b that would make the given quadrilateral a parallelogram, we need to compare opposite sides and set them equal to each other.
Let's compare the top and bottom sides:
Top side: 6b - 3
Bottom side: 5a + 1
To form a parallelogram, the top and bottom sides must be equal. So we have the equation:
6b - 3 = 5a + 1
Now let's compare the left and right sides:
Left side: 2a + 6
Right side: 3a - 10
Again, to form a parallelogram, the left and right sides must be equal. So we have the equation:
2a + 6 = 3a - 10
Now we can solve these two equations to find the values of a and b.
Equation 1: 6b - 3 = 5a + 1
Rearrange the equation to isolate b:
6b = 5a + 4
b = (5a + 4)/6
Equation 2: 2a + 6 = 3a - 10
Rearrange the equation to isolate a:
a = 16
Substitute the value of a in Equation 1:
b = (5(16) + 4)/6
b = (80 + 4)/6
b = 84/6
b = 14
Therefore, the values of a and b that would make the quadrilateral a parallelogram are:
a = 16
b = 14
To find the values of a and b that would make the quadrilateral a parallelogram, we need to consider two conditions:
1. Opposite sides of a parallelogram are equal in length.
2. Opposite sides of a parallelogram are parallel.
Let's first equate the opposite sides of the quadrilateral and set up equations based on the given information:
Top side: 6b - 3
Bottom side: 5a + 1
Left side: 2a + 6
Right side: 3a - 10
Now, we'll set up the equations using the opposite sides:
6b - 3 = 5a + 1 ... (Equation 1)
2a + 6 = 3a - 10 ... (Equation 2)
To solve Equation 2, we need to isolate the variable:
2a + 6 = 3a - 10
Subtract 2a from both sides:
6 = a - 10
Now, add 10 to both sides:
16 = a
So, we have found the value of a to be 16.
Now, substitute the value of a (16) into Equation 1:
6b - 3 = 5(16) + 1
Simplify the right side:
6b - 3 = 80 + 1
6b - 3 = 81
Now, add 3 to both sides:
6b = 84
Finally, divide both sides by 6:
b = 84/6
Solving this, we find that b = 14.
Therefore, to make the quadrilateral a parallelogram, the values of a should be 16 and b should be 14.