6. In a square ABCD, diagonals meet at O. P is a point on BC such that OB = BP.

Show that:

(i) ∠POC = 22 ½o

(ii) ∠BDC = 2 ∠POC

(iii) ∠BOP = 3 ∠CPO

5. The difference between an exterior angle of (n – 1) sided regular polygon and an exterior angle of (n + 2) sided regular polygon is 6o find the value of n.

4. The ratio between an exterior angle and an interior angle of a regular polygon is 2 : 3. Find the number of sides in the polygon.

3. AB, BC and CD are the three consecutive sides of a regular polygon. If ∠BAC = 15o; find,

(i) Each interior angle of the polygon.

(ii) Each exterior angle of the polygon.

(iii) Number of sides of the polygon.

2. In a pentagon ABCDE, AB is parallel to DC and ∠A : ∠E : ∠D = 3 : 4 : 5. Find angle E.

1. Two angles of an eight-sided polygon are 142o and 176o. If the remaining angles are equal to each other; find the magnitude of each of the equal angles.

5. Three angles of a seven-sided polygon are 132o each and the remaining four angles are equal. Find the value of each equal angle.

4. In a polygon there are 5 right angles and the remaining angles are equal to 195o each. Find the number of sides in the polygon.

3. One angle of a six-sided polygon is 140o and the other angles are equal. Find the measure of each equal angle.

2. The angles of a pentagon are in the ratio 4 : 8 : 6 : 4 : 5. Find each angle of the pentagon.