Question

the angles of a quadrilateral are in AP with common difference 20. find it angles.

Answer 1

Hey friend, ☺ here is ur answer ___________________________

plz see this attachment.
hope this helps u...

Answer 2

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

⠀⠀⠀⠀

• All angles of an quadrilateral are in AP
• Common Diff. = 20

______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

⠀⠀⠀⠀

• All angles of an AP = ??

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

⠀⠀⠀⠀

Since Sum of all angles of an quadrilateral is 360

⠀⠀⠀⠀

Therefore S = 360

⠀⠀⠀⠀

Since the no. of angles of quadrilateral is 4

⠀⠀⠀⠀

Therefore ; n = 4

⠀⠀⠀⠀

$\sf{\red{\boxed{\bold{S =\dfrac{n}{2} [ 2a + ( n - 1 ) d ] }}}}$

⠀⠀⠀⠀

$\sf :\implies\:{\bold{ 360 = \dfrac{4}{2}[ 2a + ( 4 - 1 ) 20 ]}}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf :\implies\:{\bold{ 360 = \dfrac{4}{2}[ 2a + 3 \times 20 ]}}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf :\implies\:{\bold{ 360 = 2 [ 2a + 60]}}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf :\implies\:{\bold{ \dfrac{360}{2} = [ 2a + 60 ]}}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf :\implies\:{\bold{ 180 = [ 2a + 60 ]}}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf :\implies\:{\bold{ 180 - 60 = 2a}}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf :\implies\:{\bold{ 2a = 120 }}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf :\implies\:{\bold{ a = \dfrac{120}{2} }}$

⠀⠀⠀⠀

$\sf :\implies\:{\bold{ a = 60}}$

⠀⠀⠀⠀

• Finding all angles

⠀⠀⠀⠀

Angle 1 = 60

⠀⠀⠀⠀

Angle 2 = Angle1 + 20= 60 + 20 = 80

⠀⠀⠀⠀

Angle 3 = Angle2 + 20 = 80 + 20 = 100

⠀⠀⠀⠀

Angle 4 = Angle3 + 20 = 100 + 20 = 120

⠀⠀⠀⠀

⠀⠀⠀⠀

⠀⠀⠀⠀

⠀⠀⠀⠀

______________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

⠀⠀

• All angles of an quadrilateral are 60° , 80° , 100° , 120°