Question

One angle of a quadrilateral is 2pie/9 radian and the measures of the other three angles.are in
the ratio 3:5:8 find their measures in degree.

Answer 1

⇒  Let ∠A=92π​=92π​×π180o​=40o

Let measure of other angles be 3x,5x and 8x.

So, ∠B=3x,∠C=5x and ∠D=8x

We know that sum of four angles of an quadrilateral is 360.

∴  ∠A+∠B+∠C+∠D=360

⇒  40+3x+5x+8x=360

⇒  16x=320.

⇒  x=20.

⇒  ∠B=3x=3×20=60

⇒  ∠C=5x=5×20=100

⇒  ∠D=8x=8×20=160

Measure in radian,

∠B=60×180oπ​=3π​

∠C=100×180oπ​=95π​

∠D=160×180oπ​=98π​

BRAINLYPRINCE007