Question

The angles of a quadrilateral are in Arithmetic sequence the measure of largest angle is 144 degree find the measure of other angles

Answer 1

The angles of a quadrilateral are in Arithmetic sequence. the measure of largest angle is 144°

To find : the measure of other angles.

solution : it is given that angles of the quadrilateral are in Ap.

let, a , a + d , a + 2d , a + 3d are the four angles of quadrilateral. where a and d are constants.

given largest angle = 144°

⇒(a + 3d) = 144° .......(1)

but we know, sum of angles of a quadrilateral is 360°.

so, a + (a + d) + (a + 2d) + (a + 3d) = 360°

⇒4a + 6d = 360°

⇒2a + 3d = 180° .........(2)

from equations (1) and (2) we get,

a = 180° - 144° = 36°

now d = (144° - 36°)/3 = 36°

so the angles are ;

a = 36°

a + d = 36° + 36° = 72°

a + 2d = 36° + 2 × 36° = 108°

a + 3d = 36° + 3 × 36° = 36 + 108° = 144°