Question

Angles of a quadrilateral
are in an arithmetic sequence.
Largest angle is 250. Find
the other angles.

Answer 1

Step-by-step explanation:

let the 4 angle be a-d ,a-2d , a+d, a+2d.

now in quadrilateral sum of the angle is 360

. (a-2d)+ (a-d)+ ( a+2d)+ a+d = 360

. 4a = 360

a = 360/4

a= 90

now according to question

largest angle will be a+2d

.,,.a+2d = 250

....... 90 + 2d = 250

....... 2d= 250 /90 .

....... 2d = 25/9

.........d= 25/18

now .. . a-d = 90-25/18=

........a- 2d= 90-25/9....( 2*d)

......... a+d = 90+25/18

......... a+2d= 90+ 25/9

angles are 88.61111111

......87.222222

91.3888888

250

Answer 2

Answer:

-70° , 36°7' , 143°3' , 250°

Step-by-step explanation:

Let the terms in arithmetic sequence are

a, a + d, a + 2d, a + 3d

Sum of the angles of a quadrilateral = 360°

=> a + a + d + a + 2d + a + 3d = 360°

=> 4a + 6d = 360° => 2a + 3d = 180° ---------(1)

Given, largest angle = 250 => a + 3d = 250 -----(2)

Solving (1) & (2) , a = -70° & d = 320/3

.•. required angles are -70° , 36°7' , 143°3' , 250°