Answer :
Two angles in the same parallelogram must either be equal or else add up to 180 degrees. These two are obviously not equal, so they must add up to 180.
A + B = 180
A = 180 - B (we'll use this in just a second)
A = 3B + 40
180 - B = 3B + 40
Add 'B' to each side:
180 = 4B + 40
Subtract 40 from each side:
140 = 4B
Divide each side by 4 :
35 = B
A = 180 - B = 145
A + B = 180
A = 180 - B (we'll use this in just a second)
A = 3B + 40
180 - B = 3B + 40
Add 'B' to each side:
180 = 4B + 40
Subtract 40 from each side:
140 = 4B
Divide each side by 4 :
35 = B
A = 180 - B = 145
[tex]\alpha+\beta=180^o\\\\\alpha=3\beta+40^o\\\\substitute\\\\3\beta+40^o+\beta=180^o\\4\beta=180^o-40^o\\4\beta=140^o\ \ \ \ /:4\\\beta=35^o\\\\\alpha=3\cdot35^o+40^o=105^o+40^o=145^o\\\\Solutions:35^o\ and\ 145^o.[/tex]
