Question 1154040


Each of the equal angles of an isosceles triangle is four times as large as the third angle?
What is the measure of each equal angle?
What is the measure of the third angle?

an isosceles triangle is a triangle that has two sides of equal length

both base angles are equal, {{{alpha=beta}}} 

if each of the equal angles of an isosceles triangle is four times as large as and the third angle {{{gamma}}}, we have

{{{alpha=4gamma}}}....eq.1
{{{beta=4gamma}}}.....eq.2

the sum of all angles is {{{180}}}

so, {{{alpha+beta+gamma=180}}}....eq.3

substitute {{{alpha}}} and {{{beta from eq.1 and eq.2

{{{4gamma+4gamma+gamma=180}}}

{{{9gamma=180}}}

{{{gamma=180/9}}}

{{{gamma=20}}}=> the measure of the third angle


 the measure of each equal angle:

then {{{alpha=4*20}}}=>{{{alpha=80}}} and  {{{beta=80}}}