Answer
Measure of the largest angle is $110°$
Measure of the smallest angle is $20°$
Measure of the remaining angle is $50°$
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 $90°$ more than the smallest angle.
$x=90° + y$
The measure of remaining angle is $30°$ more than the smallest angle.
$z=30° + y$
Sum of the angles of the triangle is $180°$
$x+y+z=180°$
$90° + y+y+30° + y=180°$
$120° + 3y=180°$
$ 3y=60°$
$ y=20°$
Measure of the largest angle is $x= 90° + 20° = 110°$
Measure of the smallest angle is $y= 20°$
Measure of the remaining angle is $z=30° + 20° = 50°$
