Question

The angles of a quadrilateral are in A.P whose common difference is ${10}^{\circ }$. Find the angles.

• A. ${70}^{\circ },{80}^{\circ },{90}^{\circ },{100}^{\circ }$
• B. ${60}^{\circ },{80}^{\circ },{100}^{\circ },{120}^{\circ }$
• C. ${72}^{\circ },{85}^{\circ },{98}^{\circ },{111}^{\circ }$
• D. ${75}^{\circ },{85}^{\circ },{95}^{\circ },{105}^{\circ }$

Answer 1

Answer: (D)

${75}^{\circ },{85}^{\circ },{95}^{\circ },{105}^{\circ }$

Let one of the angle is $a$
So there angles are $a+10,a+20,a+30$
$a+a+10+a+20+a+30=360$
$4a+60=360$
$4a=300$
$\therefore a=75$
First angle=${75}^{\circ }$
Second angle=$75+10={85}^{\circ }$
Third angle=$85+10={95}^{\circ }$
Forth angle=$95+10={105}^{\circ }$