Question

The measure of one angle of a parallelogram is 40 more than 3 times another. Find the measure of each angle.

Answer 1

`\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.`

Answer 2

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