Answer
Measure of the largest angle is $112°$
Measure of the smallest angle is $23°$
Measure of the remaining angle is $45°$
Work Step by Step
Let the largest angle is $x$, smallest angle is $y$ and the remaining angle is $z$
Given, the measure of largest angle is $3°$ less than $5 $ times measure of the smallest angle.
$x=5y-3°$
The measure of remaining angle is $1°$ less than twice the measure of the smallest angle..
$z=2y-1°$
Sum of the angles of the triangle is $180°$
$x+y+z=180°$
$5y-3°+y+2y-1°=180°$
$8y-4° =180°$
$ 8y=184°$
$ y=23°$
Measure of the largest angle is $x= 5(23°) -3° = 112°$
Measure of the smallest angle is $y= 23°$
Measure of the remaining angle is $z=2(23°)-1° = 45°$
