Page 219 - Start Up Mathematics_8 (Non CCE)

So, 165ºn = (n – 2) × 180º = 180ºn – 360º
360∞
fi 180ºn – 165ºn = 360º fi 15ºn = 360º fi n = = 24
15∞
Therefore, the number of sides of the regular polygon is 24.

Example 3: One of the angles of a triangle is 120º and the other two angles are equal. Find the measure
of the equal angles.
Solution: Let each equal angle of the triangle be x.

So, x + x + 120º = 180º (Sum of the angles of a D is 180º)
60∞
fi 2x + 120º = 180º fi 2x = 180º – 120º = 60º fi x = = 30º
2
Therefore, the measure of each equal angle is 30°.

EXERCISE 14.1

1. Which of the following figures are simple closed figures?

(a) (b) (c) (d) (e)

2. Which of the following figures are polygons?

(a) (b) (c) (d)

3. What will be the angle-sum of a convex polygon with (a) 11 sides (b) 16 sides?
4. If the angles of a triangle are in the ratio 2 : 3 : 4, find the angles.
5. In an isosceles triangle, the vertical angle is 40º. Find the other two angles of the triangle.
6. Draw a rough diagram to show (a) open curve (b) closed curve.
7. In ∆ JAM, if 3∠J = 4∠A = 6∠M, find all the angles.

Sum of Measure of Exterior Angles of a Polygon Extension
The sum of measure of
exterior angles of any
E 4 D polygon is 360º.
5

3 If we move forward from point A to B and then to C,
C
D, E and return to A (Fig. 14.15), one whole circle
is completed, that is 360º.
A 2
1
B So, on summing up the angles:
Fig. 14.15
–1 + –2 + –3 + –4 + –5 = 360º

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