the angles of a quadrilateral are in A.P. least angle is one-fourth the greatest angle. find the least angle
Answers
Let the 4 angles be a,a+d,a+2d and 4a (Largest angle is 4 times smallest)
Also, with common difference d,
4a=a+3d
Thus, d=a
So AP is a,2a,3a,4a
Sum of angles in quadrilateral should be 360
a+2a+3a+4a=360
10a=360
a=36
Least angle is 36 deg
Given : angles of a quadrilateral are in ap the least angle is one fourth of the greatest angle.
To find : least angle
Solution:
Let say 4 angles in AP are
a , a + d , a + 2d , a + 3d
Sum of angles of a quadrilateral is 360°
=> a + a + d + a + 2d + a + 3d = 4a + 6d = 360
=> 2a + 3d = 180
least angle is one fourth of the greatest angle
=> a = (1/4)(a + 3d)
=> 4a = a + 3d
=> 3a = 3d
=> a = d
2a + 3d = 180
=> 2a + 3a = 180
=> 5a = 180
=> a = 36
a = d => d = 36
Hence angles of the quadrilateral
36° , 72° , 108° , 144°
least angle 36°
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