Answered

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

Sagot :

AL2006
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
[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]
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