Answer:
4 a + 2b = 360 ----->equation 1
a + b = 116 --------> equation 2
a = 64 °
b = 52°
Step-by-step explanation:
The sum of all of the internal angles would be 360°. Since we have four "a"s and two "b"s, we have:
4a + 2b = 360
Then told that the largest internal angle of the parallelogram is 116 degrees, so:
a + b = 116
We now have a system of two equations and two unknowns.
I'll simplify the first equation by dividing both sides by 2, then multiplying the second equation by -1 to prepare for solving by elimination:
2a + b = 180
-a - b = -116
---------------------- Add the equations together to get:
a = 64°
Now we can solve for b:
a + b = 116
64 + b = 116
b = 52°
So the values of "a" and "b" are:
a = 64° and b = 52°
Hope this helped :)
