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6. In a square ABCD, diagonals meet at O. P is a point on BC such that OB = BP.
(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.
(i) Let each angle of measure x degree.
Therefore, measure of each angle will be:
x – 180o – 2 × 15o = 150o
(ii) Let each angle of measure x degree.
Therefore, measure of each exterior angle will be:
x = 180o – 150o
(iii) Let the number of each sides is n.
Now we can write
n . 150o = (2n – 4) × 90o
180o n – 150o n = 360o
300 n = 360o
n = 12
Thus, the number of sides are 12.
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.
Let the measure of each equal sides of the polygon is x.
Then we can write:
142o + 176o + 6x = (2 × 8 – 4) 90o
6x = 1080o – 318o
6x = 762o
x = 127o
Thus, the measure of each equal angles is 127o