Question 792097
The two equal angles (the base angles) are each 2/15 of what angle?
A straight angle (a {{{180^o}}} angle)?
The vertex angle of the isosceles triangle?
 
OPTION 1:
If each the base angles measures {{{2/15}}} as much as a straight angle, we do not even need an equation to find the measure of those angles. The measure of each base angle would be
{{{180^o *(2/15)=24^o}}}.
Then, if we can call the measure of the remaining angle {{{x}}}.
{{{42^o+42^o+x=180^o}}}
{{{84^o+x=180^o}}}
{{{x=180^o-84^o}}}
{{{x=96^o}}}
 
OPTION 2:
If each the base angles measures {{{2/15}}} as much as the vertex angle, the measures are not going to be whole numbers.
 
{{{x}}}= measure of the vertex angle of the isosceles triangle (in degrees)
  
The summ of the measures of the angles in any triangle is {{{180^o}}}, so
{{{(2/15)x+(2/15)x+x=180}}} is our equation.
 
Simplifying and solving:
{{{(2/15)x+(2/15)x+x=180}}}
{{{(2/15)x+(2/15)x+1*x=180}}}
{{{(2/15+2/15+1)x=180}}}
{{{(2/15+2/15+15/15)x=180}}}
{{{((2+2+15)/15)x=180}}}
{{{(19/15)x=180}}}
Multiplying times 15 both sides of the equal sign, we get
{{{19x=180*15}}}
{{{19x=2700}}}
{{{x=2700/19}}} (about {{{142.1^o}}})
Then, each of the other two angles would measure
{{{(2/15)(2700/19)=2*2700/(15*19)=36/19}}} (about {{{18.95^o}}})