Question 182998
Let a, b and c be the 3 angles.  Since there are 3 variables, we're gonna need (at least) 3 equations to solve for them.  Being a triangle we know:

Equation 1:  {{{ a + b + c = 360 }}}
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"one angle is double the measure of a second angle":

Equation 2:  {{{ a = 2b }}}
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"but is 10 degrees less than the measure of the third angle":

Equation 3:  {{{ a = c - 10 }}}
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Let's re-write equations 2 & 3 in terms of "a" so we can substitute them into equation 1.
Equation 2 can be rewritten as:
{{{ b = a/2 }}}

Equation 3 can be rewritten as:
{{{ c = a + 10 }}}
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Substituting back into Equation 1 gives us:
{{{ a + (a/2) + (a + 10) = 360 }}}

I prefer not to work with fractions if I can help it, so let's multiply every element, on both sides, by 2:
{{{ 2a + a + 2a + 20 = 720 }}}

Group the a's:
{{{ 5a + 20 = 720 }}}

Subtract 20 from both sides:
{{{ 5a = 700 }}}

Divide both sides by 5:
{{{ a = 140 }}}
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Now we can substitute a back into our "modified" Equations 2 & 3 to solve for b & c:
Equation 2:  {{{ b = a/2 }}}
{{{ b = (140) / 2 }}}
{{{ b = 70 }}}

Equation 3:  {{{ c = a + 10 }}}
{{{ c = (140) + 10 }}}
{{{ c = 150 }}}
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So our angles are <b>140</b>, <b>70</b> and <b>150</b>.
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Hope this helps. ~ Joe