Math  /  Algebra

Questiona) Given that the line joining the points A(a,5)A(a, 5) and B(2,b)B(-2, b) have a slope of 2 and that the gradient of the line joining the points B and C(b,a)C(-b, a) is 2 , find the values of aa and bb. [9 marks] b) The interior angle of a regular polygon exceeds its exterior angle by 108108^{\circ}. How many sides does the polygon have? [11 marks]

Studdy Solution
Use the relationship between interior and exterior angles.
The sum of the interior and exterior angles of a polygon is 180 180^\circ .
Let x x be the exterior angle. Then the interior angle is x+108 x + 108^\circ .
x+(x+108)=180 x + (x + 108^\circ) = 180^\circ 2x+108=180 2x + 108^\circ = 180^\circ 2x=180108 2x = 180^\circ - 108^\circ 2x=72 2x = 72^\circ x=36 x = 36^\circ
The exterior angle of a regular polygon is given by:
360n=36 \frac{360^\circ}{n} = 36^\circ
Solving for n n :
n=36036 n = \frac{360^\circ}{36^\circ} n=10 n = 10
The polygon has:
10 \boxed{10} sides.

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