The angles of a quadrilateral are in AP

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 $105^{\circ}$.

 

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