The sum of the interior angles of any quadrilateral is always 360∘. So, for this quadrilateral, the sum of the given angles can be written as: (x+15)+(2x−45)+(x−30)+(x+10)=360 Now, simplify the equation: x+15+2x−45+x−30+x+10=360 Combine like terms: x+2x+x+x+(15−45−30+10)=360 5x−50=360
Now, solve for x : 5x=360+50 5x=410 x=
410
5
x=82 Now substitute x=82 into the expressions for the angles: x+15=82+15=97∘ 2x−45=2(82)−45=164−45=119∘ x−30=82−30=52∘ x+10=82+10=92∘ The four angles are 97∘,119∘,52∘, and 92∘. The least interior angle is 52∘.