These quadrilaterals were convex. What would happen, if the quadrilateral is not convex? Consider quadrilateral ABCD. Split it into two triangles and find the sum of the interior angles in adjoining figure.

3

(a)

Find x + y + z

3

(a)

Find x, in the following figures.

3

(a)

The sides of a pentagon are produced in order and the exterior angles, so obtained are of measure x⁰ ,(3x)⁰ ,(4x + 10)⁰, (2x +5)⁰ and (5x)⁰ ,respectively. Find the value of x and measure of each exterior angle of a pentagon.

3

(a)

In a trapezium FARE, EP and RP are bisectors of ㄥE and ㄥR, respectively. Find ㄥFAR and ㄥEFA.

3

(a)

Find the measure of each interior angle of a regular
(a) pentagon
(b) octagon.

3

(a)

If an angle of a parallelogram is two-third of its adjacent angle, then find the smallest angle of the paralleloqrarn.

3

(a)

In a rhombus ABCD, if AB = 10 cm and BD = 16 cm, then find the length of diagonal AC .

3

(a)

Find the measure of each interior angle of a regular heptagon.

3

(a)

In the adjoining figure, find x + y + z + w.

3

(a)

In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1: 2 : 3: 4. Find the measure of each angle of the quadrilateral.

3

(a)

The measures of two adjacent angles of a parallelogram are in the ratio 4:5. Find the measure of each of the angles of the parallelogram.

3

(a)

In a quadrilateral ABCD, DO and CO are the bisectors of \(\angle\)D and \(\angle\)C respectively. Prove that \(\angle\)COD = \(\frac { 1 }{ 2 } \)[\(\angle\)A + \(\angle\)B].

3

(a)

Take a thick white sheet.
Fold the paper once.
Draw two line segments of different lengths as shown in the figure.

Cut along the line segments and open up.
You have the shape of a kite.
Has the kite any line symmetry?
Fold both the diagonals of the kite. Use the set-square to check if they cut at right angles. Are the diagonals equal in length?

Verify by (paper-folding or measurement) if the diagonals bisect each other.
By folding an angle of the kite on its opposites, check for angles of equal measure. Observe the diagonal folds; do they indicate any diagonal being an angle bisector? Share your findings with others and list them.

3

(a)

Show that \(\Delta\) ABC and \(\Delta\) ADC are congruent. What do we infer from this?

3

(a)