Answer:
b is 10 degrees and a is 64 degrees.
Step-by-step explanation:
Properties of a parallelogram needed for this problem: Opposite angles are congruent and adjacent angles are supplementary, meaning they add to 180 degrees.
This means that in the picture, 2a and 12b+8 are equal, while 2a and 5b+2 are supplementary.
From this we can make two equations:
2a=12b+8
and
2a+5b+2=180
If we subtract 5b+2 in the second equation, both equations will equal 2a. I'll explain why that's good. We end up with:
2a=12b+8
and
2a=180-5b-2
Now, we can set the two equations equal to each other because they both equal the same thing. Then simplify.
12b+8=180-5b-2
17b=170
b=10
Knowing b is 10 degrees, we can easily plug that back into one of our original two equations. I'll choose 2a=12b+8.
2a=12(10)+8
2a=120+8
2a=128
a=64
b is 10 degrees and a is 64 degrees.
