Question

If the angles of a quadrilateral EFGH, taken in order, are in the ratio of
7 : 3 : 4 : 6, which type of quadrilateral is EFGH and why ?

Answer 1

Given ratio of the angles of a quadrilateral is 7:3:4:6
Let the angles be 7x,3x,4x,6x
sum of the angles in a quadrilateral is 360°
⇒7x+3x+4x+6x = 360°
⇒20x=360°
⇒x=360/20
⇒x = 18°
Therefore the angles are 7(18),3(18),4(18),6(18)
⇒126°,54°,72°,108°
EFGH is a cyclic quadrilateral .

Answer 2

The angles of the quadrilateral are 7x,3x,4x and 6x
sum of all angles in a quadrilateral is 360
therefore,
7x+3x+4x+6x=360
20x=360
x=18degrees
the angles are therefore
7(18),3(18),4(18),6(18)
=126,54,72,108

so...since the opposite angles are supplementery..that is,
126+54=180
108+72=180
therefore it is a cyclic quadrilateral