Consider a concave quadrilateral ABCD, Split it into two triangles and find the sum of the interior angles.

Take any quadrilateral, say ABCD , Divide it into two triangles, by drawing a diagonal. You get six angles 1,2,3,4,5 and 6. Use the angle sum property of a triangle and argue how the sum of the measures of and amount to 180^@ + 180^@ = 360^@ .

We know that parallelogram is also a quadrilateral. Let us also split such a quadrilateral into two triangles, find their areas ad hence that of the parallelogram . Does this agree with the formula that you know already?

Take four congruent card-board copies of any quadrilateral ABCD, with angles as shown in the figures. Arrange the copies as shown in the figure, where angles angle1, angle2,angle3,angle4 meet at a point. What can you say about the sum of the angles angle1, angle2,angle3 and angle4 .

Take four congruent card-board copies of any quadrilateral ABCD, with angles as shown in the figures. Arrange the copies as shown in the figure, where angles angle1, angle2,angle3,angle4 meet at a point. What can you say about the sum of the angles angle1, angle2,angle3 and angle4 .

Two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60^@ . If the third side is 3, find the fourth side.

A(-4,-2),B(-3,-5),C(3,-2) and D(2,k) at the vertices of a quadrilateral ABCD. Find the value of k if the area of the quadrilateral is 28 square unit.

Can a quadrilateral ABCD be a parallelogram, if angleD + angleB = 180^@ ?

A(0,0), B(6,0), C(4,3) and D(0,k) are the vertices of a quadrilateral ABCD .Find the value of k if the area of quadrilateral is 14 sq.units.

The angles of a triangle are in the ratio 1:3:5. Find them in radian

Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.) What can you say about the angle sum of a convex polygon with number of sides? 7