The angles of a quadrilateral are in ap and th greatest angle is double the least angle in radius
Answers
Hi there !
The angles of a quadrilateral are in AP, and the greatest angle is double the least.So,
Let a be the least angle and common difference let it be d.
Angle will be a,a+d , a+2d and a +3d
(Given that the angles of a quadrilateral are in A.P)
→ a+ a+d+ a+2d+ a+3d = 360 [ •°• Property of quadrilateral ]
→ 4a + 6d = 360
Taking two as common,
2a+3d= 180-----(1)
Now, according to question, the greatest angle is double the least.
Greater one is = a+3d
Smallest one is = a
So, forming equation
a+3d (greatest angle) = 2 ×a (smallest angle)
a+ 3d = 2a-------(2)
From equation (2),
a= 3d
Put a in (1) equation.
2a + a = 180
=> 3a = 180
a= 60°
Now solving equation 3d = a by putting a = 60
d = 20
So, the four angles are 60, 80, 100, 120.
Read more on Brainly.in - https://brainly.in/question/11505916#readmore
Thankyou :)