Question

Three angles of a quadrilateral are 57°, 40° and 62° repectively. Find the fourth

angle. Is this quadrilateral a convex or a concave polygon? Give reasons.​

Answer 1

Answer:

let the fourth side be x.

Step-by-step explanation:

So we have,

57°+40°+62°+x = 360°

=> 159° + x= 360°

=> x= 360°-159°

=> x= 201°

A quadrilateral is a four sided polygon that can be classified in several categories based on its properties. Quadrilaterals can be categorized as convex or concave. If the quadrilateral has an interior angle greater than 180 degrees, it is concave.

Answer 2

Let the fourth side be x.

So we have,

57°+40°+62°+x = 360°  ------(∵ sum of four angles of quadrilateral is 360)

             159° + x= 360°

                        x= 360°-159°

                        x= 201°

∴ the fourth angle is 201°.

∵ the quadrilateral has an interior angle greater than 180 degrees,

∴ it is concave.