Question

CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM. I HAVE TO SOLVE FOR A AND B

Answer 1

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.