Answer
Angles are $70°, 70°,100°,120°$.
Work Step by Step
Let four angels of the quadrilateral be $x°, y°, z°$ and $w°$.
Two smallest angles be $x°$ and $y°$. They have same measure. So,
$x° = y°$ Equation $(1)$.
Third angle $(z°)$ measures $30°$ more than the measure of one of the smallest angle.
$z°= x° + 30°$ Equation $(2)$
Fourth angle $(w°)$ measures $50$ more than the one of the smallest angle then
$w° = x° + 50°$ Equation $(3)$
Sum of the measures of the quadrilateral is $360°$
$x°+y°+z°+w° = 360°$ Equation $(4)$
Substituting the values from Equations $(1)$, $(2)$, $(3)$ in Equation $(4)$, we get
$x°+y°+z°+w° = 360°$
$x°+x°+x°+30°+x°+50° = 360°$
$4x° +80° = 360°$
$4x° = 360° - 80°$
$4x° = 280°$
$x° = 70°$
$ y° = x° = 70° $
$z°= x° + 30° = 70° + 30° = 100°$
$w° = x° + 50° = 70° + 50° = 120°$
Angles are $70°, 70°,100°,120°$.
