Question 733740


An isosceles triangle is a triangle with (at least) two equal sides,  then base  angles  are congruent.

let the two equal angles be {{{alpha}}} and {{{beta}}}

so,{{{alpha=beta}}}

third angle is {{{gamma}}}


if the third angle of an isosceles triangle is {{{16}}} dgree less than the sum of the two equal angles, then 

{{{alpha +beta=gamma +16}}}......since {{{alpha=beta}}}, we have

{{{2*alpha =gamma +16}}}..solve for {{{gamma}}}

{{{2alpha-16 =gamma }}}

we know that the sum of all three angles in triangle is {{{180}}}

then we have:

{{{alpha +beta +gamma=180}}}.......substitute {{{gamma}}} and {{{beta}}}

{{{alpha +alpha +(2alpha-16)=180}}}....solve for {{{alpha}}}

{{{alpha +alpha +2alpha-16=180}}}

{{{4alpha=180+16}}}

{{{4alpha=196}}}

{{{alpha=196/4}}}

{{{highlight(alpha=49)}}}

then {{{highlight(beta=49)}}}

and

{{{gamma=2*49-16  }}}

{{{gamma=98-16  }}}

{{{highlight(gamma=82)  }}}