The angles of a quadrilateral are in AP whose common difference is 10∘. Find the smallest angle of the quadrilateral.
Answer:
75∘
- The angles of the quadrilateral are in AP with the common difference of 10∘.
Let the angles be x,x+10∘,x+20∘, and x+30∘. - We know that the sum of all angles of a quadrilateral is 360∘. Thus x+x+10∘+x+20∘+x+30∘=360∘⟹4x+60∘=360∘⟹4x=360∘−60∘⟹4x=300∘⟹x=300∘4⟹x=75∘
- Let us now substitute the value of x to get the four angles. x=75∘x+10∘=75∘+10∘=85∘x+20∘=75∘+20∘=95∘x+30∘=75∘+30∘=105∘
- Hence, the smallest angle of the quadrilateral is 75∘ .