one angle of a parrallelogram is 23 degrees less than six times the measure of the angle next to it.the sum of the measures of the angles is 180 degrees. find the measure of the adjacent angles of the parrallelogram.
if one angle is x, then
x + 6x-23 = 180
7x = 203
x = 29
the two angles are 29 and 151 degrees
new formula of parallelogram
To find the measure of the adjacent angles of a parallelogram, we'll set up an equation based on the given information.
Let's call the measure of the angle next to the angle in question "x". According to the problem, one angle is 23 degrees less than six times the measure of the angle next to it. So we can write the equation:
Measure of the angle = 6x - 23
Since we know that the sum of the measures of the angles in a parallelogram is 180 degrees, we can also set up another equation:
Measure of the angle + Measure of the angle next to it = 180
Plugging in the value we found for the measure of the angle:
(6x - 23) + x = 180
Now we can solve the equation:
7x - 23 = 180
Adding 23 to both sides:
7x = 203
Dividing both sides by 7:
x = 29
So the measure of the angle next to the angle in question is 29 degrees.
To find the measure of the angle itself, we substitute the value of x back into the equation:
Measure of the angle = 6x - 23 = 6(29) - 23 = 174 - 23 = 151
Thus, the measure of the adjacent angles of the parallelogram is 29 degrees and 151 degrees.