Question 1004851


An isosceles triangle is a triangle with (at least) two equal sides.

in your case, base angles are same 

let's the base angles be {{{alpha}}} and {{{beta}}}, and the {{{vertex}}} angle {{{gamma}}}

if the measure of each of the base angle is {{{9}}}° less than {{{4}}} times the measure of the {{{vertex}}} angle, we have
{{{alpha=4gamma-9}}}
{{{beta=4gamma-9}}}

since {{{alpha+beta+gamma=180}}} we have

{{{4gamma-9+4gamma-9+gamma=180}}}

{{{9gamma-18=180}}}

{{{9gamma=180+18}}}

{{{9gamma=198}}}

{{{gamma=198/9}}}

{{{gamma=22}}}

now find {{{alpha}}} and {{{beta}}}

{{{alpha=4gamma-9}}}

{{{alpha=4*22-9}}}

{{{alpha=88-9}}}

{{{alpha=79}}} and {{{beta=79}}}

so, your angles are:{{{79}}},{{{79}}}, and {{{22}}}