Question

One angle of a quadrilateral has measure `(2pi^"c")/5` and the measures of other three angles are in the ratio 2 : 3 : 4. Find their measures in degree and radian.

Answer 1

Let ABCD be the quadrilateral such that 

m∠A = `(2pi^"c")/5`

= `((2pi)/5 xx 180/pi)^circ`

= 72°

Since the other three angles are in the ratio 2: 3: 4

let these angles be 2k, 3k, 4k in degrees.

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

72° + 2k + 3k + 4k = 360°

∴ 9k = 360° – 72° = 288°

∴ k = 32°

The measures of the angles in degrees are

∴ 2k = 2 x 32° = 64°

3k = 3 x 32° = 96°

4k = 4 x 32° = 128°

Now, θ° = `(θxxpi/180)^"c"`

∴ The measures of the angles in radians are

64° = `(64 xx pi/180)^"c" = ((16pi)/45)^"c"`

96° = `(96 xx pi/180)^"c" = ((8pi)/15)"c"`

128° = `(128 xx pi/180)^"c" = ((32pi)/45)^"c"`