Algebra - Find the values of a and b that would make the quadrilateral
a parallelogram.
Top left - 5b+6
Bottom left - 4a-8
Bottom right - 8a-10
Pls help
I assume these are angles
Opposite angles are congruent, and consecutive angles are supplementary, so
5b+6 = 8a-10
4a-8 + 8a-10 = 180
solve these to get
a = 33/2
b = 116/5
To determine the values of a and b that would make the quadrilateral a parallelogram, we need to use the properties of a parallelogram.
One property of a parallelogram is that opposite sides are equal in length. Therefore, we can set up equations using this property:
Top left side = Bottom right side
5b + 6 = 8a - 10 (Equation 1)
Bottom left side = Top right side
4a - 8 = 8a - 10 (Equation 2)
Now, we can solve these equations simultaneously to find the values of a and b.
From Equation 1, we can isolate b:
5b = 8a - 16
b = (8a - 16)/5
Substituting this value of b into Equation 2, we can solve for a:
4a - 8 = 8a - 10
4a - 8a = -10 + 8
-4a = -2
a = (-2)/(-4)
a = 1/2
Now that we have found the value of a, we can substitute it back into Equation 1 to solve for b:
b = (8*(1/2) - 16)/5
b = (4 - 16)/5
b = (-12)/5
Therefore, the values of a and b that would make the quadrilateral a parallelogram are:
a = 1/2
b = -12/5