Question

Help! How do I solve this??

Answer 1

`a = 32, \ b = 20`

Explanation:

124 degree angle and "3a - 2b" angle are supplementary (in a straight line -- add upto 180 degrees). So we can say and write:

124 + "3a - 2b" = 180

3a - 2b = 180 - 124

3a - 2b = 56

Now,

"2a + 3b" and "3a - 2b" are also supplementary. So we can write:

2a + 3b + 3a - 2b = 180

5a + b = 180

Lets solve this 2nd equation for b:

5a + b = 180

b = 180 - 5a

We put this into 1st equation and solve for a:

3a - 2b = 56

3a - 2(180 - 5a) = 56

3a - 360 +10a = 56

13a = 56 + 360

13a = 416

a = 416/13

a = 32

Now, finding b:

b = 180 - 5a

b = 180 - 5(32)

b = 20

So,

a = 32, b = 20