Quadrilateral part 4

Angles of a quadrilateral are (4x)^@, 5(x+2)^@, (7x-20)^@ and 6(x+3)^@ . Find: (i) the value of x. (ii) each angle of the quadrilateral.

The co-ordinates of the four vertices of quadrilateral are (-2,4),(-1,2), (1, 2) and (2, 4), taken in order. The equation of the line through the vertex (-1, 2) and dividing the quadrilateral in two equal parts is:

The angles of a quadrilateral are in the ratio 3: 4: 5: 6 . Show that the quadrilateral is a trapezium.

Three angles of a quadrilateral are in the ratio 4:6:3. If the fourth angle is 100^(@) find the three angles of the quadrilateral.

Three angles of a quadrilateral are in the ratio 4:6:3. If the fourth angle is 100^@ , find the ther three angles of the quadrilateral.

If the sides of a cyclic quadrilateral are 3,3,4,4, show that a circle be inscribed in it.

The four vertices of a quadrilateral are (1,\ 2),\ (-5,\ 6),\ (7,\ -4) and (k ,\ -2) taken in order. If the area of the quadrilateral is zero, find the value of k .

The angles of a quadrilateral are in the ratio 4:3:6:5. Show that it is a trapezium.

If the angles of quadrilateral are in ratio of 1:2:4:5 then largest angle is

If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.