Advertisement Remove all ads

Answer the following : The angles of a quadrilateral are in A.P. and the greatest angle is double the least. Find angles of the quadrilateral in radian. - Mathematics and Statistics

Sum

Answer the following :

The angles of a quadrilateral are in A.P. and the greatest angle is double the least. Find angles of the quadrilateral in radian.

Advertisement Remove all ads

Solution

Let the angles of the quadrilateral be

a – 3d, a – d, a + d, a + 3d in degrees.

Since sum of all the angles of the quadrilateral is 360°,

a – 3d + a – d + a + d + a + 3d = 360°

∴ 4a = 360°

∴ a = 90°

According to the given condition, the greatest angle is double the least.

∴ a + 3d = 2(a – 3d)

∴ 90° + 3d = 2(90° – 3d)

∴ 90° + 3d = 180° – 6d

∴ 9d = 90°

∴ d = 10°

∴ the angles of the quadrilateral are

a – 3d = 90° – 3(10°) = 90° − 30° = 60°

a – d = 90° – 10° = 80°

a + d = 90° + 10° = 100°

a + 3d = 90° + 3(10°) = 90° + 30° = 120°

Now, θ° = `(θxxpi/180)^"c"`

∴ The measures of the angles in radians are

∴ 60° = `(60 xx pi/180)^"c" = pi^"c"/3`

80° = `(80 xx pi/180)^"c" = (4pi^"c")/9`

100° = `(100 xx pi/180)^"c" = (5pi^"c")/9`

120° = `(120 xx pi/180)^"c" = (2pi^"c")/3`

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 1 Angle and its Measurement
Miscellaneous Exercise 1 | Q 2. II (11) | Page 13
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×