Question:
The angles of a quadrilateral are in AP whose common difference is 10°. Find the angles.
Solution:
To Find: The angles of a quadrilateral.
Given: Angles of a quadrilateral are in AP with common difference $=10^{\circ}$.
Let the required angles be $a,\left(a+10^{\circ}\right),\left(a+20^{\circ}\right)$ and $\left(a+30^{\circ}\right)$
Then, $a+\left(a+10^{\circ}\right)+\left(a+20^{\circ}\right)+\left(a+30^{\circ}\right)=360^{\circ} \Rightarrow 4 a+60^{\circ}=360^{\circ} \Rightarrow a=75^{\circ}$
NOTE: Sum of angles of quadrilateral is equal to $360^{\circ}$
So Angles of a quadrilateral are $75^{\circ}, 85^{\circ}, 95^{\circ}$ and $105^{\circ}$.