Question:
The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.
Solution:
Let the angles be $(A)^{\circ},(A+d)^{\circ},(A+2 d)^{\circ},(A+3 d)^{\circ}$.
Here, d = 10
So, $(A)^{\circ},(A+10)^{\circ},(A+20)^{\circ},(A+30)^{\circ}$ are the angles of a quadrilateral whose sum is $360^{\circ}$.
$\therefore(A)^{\circ},(A+10)^{\circ},(A+20)^{\circ},(A+30)^{\circ}=360^{\circ}$
$\Rightarrow 4 A=360-60$
$\Rightarrow A=\frac{300}{4}=75^{\circ}$
The angles are as follows:
$75^{\circ},(75+10)^{\circ},(75+20)^{\circ},(75+30)^{\circ}$, i. e. $75^{\circ}, 85^{\circ}, 95^{\circ}, 105^{\circ}$