Question 72825
Let f=first angle, s=second angle, t=third angle
{{{f=2s}}} the measure of the first angle is twice the measure of the second angle
{{{t=s-20}}}he measure of the third angle is 20 degrees less than the second angle
{{{f+s+t=180}}}The sum of all of the angles in a triangle equal 180 degrees
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Plug in f=2s into f and plug in t=s-20 into t of {{{f+s+t=180}}}
{{{highlight(2s)+s+highlight(s-20)=180}}}Notice how I substituted to have only one variable in the equation
{{{2s+s+s-20=180}}}solve for s
{{{4s-20=180}}}Add like terms
{{{4s=200}}}
{{{s=50}}}
Plug s=50 into f=2s
{{{f=2(50)}}}
{{{f=100}}}
Plug s=50 into t=s-20
{{{t=50-20}}}
{{{t=30}}}
So the 1st angle is 100 degrees, the 2nd angle is 50 degrees, and the 3rd angle is 30 degrees
Check:
{{{100+50+30=180}}}
{{{180=180}}}Works