The measure of the supplement of an angle is 20° more than three times the measure of the original angle. What are the measures of the angles?

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Answer 1 · 2017-02-27T15:53:10

The original angle is $40^@$ .
Its supplement is $140^@$

Recall that the sum of supplemental angles is $180^@$ .

Based on the question, an expression can be set up with a variable.

If $x$ is the value of the original angle, and $(3x+20)$ is equal to its supplement, then
$180=x+(3x+20)$

Solving for x, we get:
$180=4x+20$

$160=4x$

$40=x$

The original angle is $40^@$ .

To find the supplement, plug in 40 to the expression that we defined above. The supplement is equal to:
$=3*(40)+20$

$=120 + 20=140$

Its supplement is $140^@$

To check, verify that the two angle measurements meet the definition, meaning they sum to $180^@$

$140^@+40^@=180^@$