Question
The angle of a quadrillateral are A.P. with common difference 20°.find its angles.
✓
Answer
Let the four angle of a quadrilateral in AP.be a,
$a+20^{\circ}, a+40^{\circ}$ and $a+60^{\circ}$
$\therefore a+\left(a+20^{\circ}\right)+\left(a+40^{\circ}\right)+\left(a+60^{\circ}\right)=360^{\circ}.......$ (Angle sum property)
$\Rightarrow 4 a+120^{\circ}=360^{\circ}$
$\Rightarrow 4 a=240^{\circ}$
$\Rightarrow a=60^{\circ}......(1)$
Thus, angles of a quarilateral are $=a, a+20^{\circ}, a+40^{\circ}$ and $60^{\circ}$
$=60^{\circ}, 80^{\circ}, 100^{\circ}$ and $120^{\circ}$
$a+20^{\circ}, a+40^{\circ}$ and $a+60^{\circ}$
$\therefore a+\left(a+20^{\circ}\right)+\left(a+40^{\circ}\right)+\left(a+60^{\circ}\right)=360^{\circ}.......$ (Angle sum property)
$\Rightarrow 4 a+120^{\circ}=360^{\circ}$
$\Rightarrow 4 a=240^{\circ}$
$\Rightarrow a=60^{\circ}......(1)$
Thus, angles of a quarilateral are $=a, a+20^{\circ}, a+40^{\circ}$ and $60^{\circ}$
$=60^{\circ}, 80^{\circ}, 100^{\circ}$ and $120^{\circ}$
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