Question 743699
Let {{{ a[1] }}}, {{{ a[2] }}} and {{{ a[3] }}} be the angles in the triangle


Total angles in a triangle always add up to 180 so
{{{ a[1]+a[2]+a[3]=180 }}} [1]


"One angle of a triangle is 3 times as large as another"
{{{ a[1]=3a[3] }}} [2]


"The measure of the third angle is 40 degrees greater than that of the smallest angle"
{{{ a[2]=a[3]+40 }}} [3]


substituting for {{{ a[3] }}} in [1] using [2] and [3] gives

{{{ 3a[3] + (a[3] + 40) +a[3] = 180 = 5a[3] + 40 }}}

hence
{{{ 5a[3] = (180-40) }}}

or

{{{ a[3] = 140/5 = 28 )))


Using [2] we get
{{{ a[1] = 3a[3] = 3 x 28 = 84 }}}


Using [3] gives
{{{ a2 = a[3]+40 = 28 + 40 = 68 }}}


Checking in [1]
a[1], a[2], a[3] = 84 + 68 + 28  = 180 QED

The 3 angles are 28, 68 and 84 degrees.