Question

Find the values of a and b

Answer 1

a=15, b=14

Explanation:

We know all angles must add up to 360, so lets add all angles and set them equal to 360.

`7a+33+3b+10a-12+6b-42=360\\17a+9b-21=360`

We also know that any angle opposite another is equal. Lets take 6b-42 and 3b and set them equal.

`3b=6b-42`

Now solve for b in both equations

`3b=6b-42\\-3b=-42\\b=14`

`17a+9b-21=360\\9b-21=360-17a\\9b=381-17a\\b=(381-17a)/(9)`

Now we set the two equations equal to each other to solve for a:

`14=(381-17a)/(9) \\126=381-17a\\-255=-17a\\15=a`

This gives a=15, b=14.