in a parallelogram, consecutive angles aresupplementary. in the parallelogram below angle F measures (6x + 1) degrees and angle G measures (8x +11) degrees. find the numerical measure of both angles.
To find the numerical measure of angles F and G in the parallelogram, we can use the fact that consecutive angles in a parallelogram are supplementary.
Supplementary angles add up to 180 degrees. Therefore, we can set up the equation:
(6x + 1) + (8x + 11) = 180
Simplifying the equation, we combine like terms:
14x + 12 = 180
Next, we isolate the variable by subtracting 12 from both sides:
14x = 168
Finally, we solve for x by dividing both sides by 14:
x = 168 / 14
x = 12
Now that we have the value of x, we can substitute it back into the expressions for angles F and G to find their numerical measures:
Angle F = 6x + 1 = 6(12) + 1 = 73 degrees
Angle G = 8x + 11 = 8(12) + 11 = 107 degrees
So, angle F measures 73 degrees and angle G measures 107 degrees.