6.) Two consecutive angles of a parallelogram are supplementary opposite angles have measures 2(3x + 20) and 4(x + 5), respectively. What are the measures of each congruent in the parallelogram?
To find the measures of each congruent angle in the parallelogram, we need to use the given information about supplementary opposite angles.
Let's denote the measure of one of the congruent angles as y. Since opposite angles in a parallelogram are congruent, the measure of the other congruent angle will also be y.
According to the given information:
1) Two consecutive angles of a parallelogram are supplementary. This means that the sum of their measures is 180 degrees. Therefore, we have the equation:
2(3x + 20) + 4(x + 5) = 180
2) Now we can solve this equation to find the value of x:
2(3x + 20) + 4(x + 5) = 180
6x + 40 + 4x + 20 = 180
10x + 60 = 180
10x = 180 - 60
10x = 120
x = 120/10
x = 12
3) Now that we have found the value of x, we can substitute it back into the expressions for the measures of the opposite angles:
Angle 1: 2(3x + 20)
= 2(3 * 12 + 20) [Substitute x = 12]
= 2(36 + 20)
= 2(56)
= 112 degrees
Angle 2: 4(x + 5)
= 4(12 + 5) [Substitute x = 12]
= 4(17)
= 68 degrees
Therefore, the measures of each congruent angle in the parallelogram are 112 degrees and 68 degrees.