Question 762194
Let A = the first angle
Let B = the second angle
Let C = the third angle
Equation 1: {{{A + B + C = 180}}}
Equation 2: {{{A = B + 24}}}
Equation 3: {{{C = 4B}}}
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Note that equations 2 & 3 are solved in terms of B.
Plug (B + 24) into equation 1 for A and plug (4B) into equation 1 for C.
Equation 1: {{{A + B + C = 180}}}
{{{(B + 24) + B + (4B) = 180}}}
Combine like terms.
{{{6B + 24 = 180}}}
Subtract 24 from both sides.
{{{6B = 156}}}
Divide both sides by 6.
{{{highlight(B = 26)}}}
Using 26 for B, solve for A & C.
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Equation 2: {{{A = B + 24}}}
{{{A = (26) + 24}}}
{{{highlight_green(A = 50)}}}
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Equation 3: {{{C = 4B}}}
{{{C = 4*(26)}}}
{{{highlight(C = 104)}}}
The largest angle is 104 degrees.