Page 182 - ICSE Math 8

Example 2: Three angles of a quadrilateral are in the ratio 3 : 5 : 7. The difference of the least and the
greatest of these angles is 76º. Find all the four angles of the quadrilateral.
Solution: Let the three angles of the quadrilateral be 3x, 5x, 7x.
The difference of the least and the greatest of these angles is 76º.
76∞
fi 7x – 3x = 76º fi 4x = 76º fi x = = 19º
4
So, the three angles are 3 × 19º, 5 × 19º and 7 × 19º, i.e., 57º, 95º and 133º.
Let the fourth angle be y.
We know that the sum of four angles of a quadrilateral = 360º
fi 57º + 95º + 133º + y = 360º fi 285º + y = 360º fi y = 360º – 285º = 75º
Therefore, the four angles of the quadrilateral are 57º, 95º, 133º and 75º.

Example 3: Find the measure of each exterior angle of a regular polygon with: (a) 9 sides (b) 15 sides

Solution: Sum of all exterior angles of a regular polygon = 360º
360∞
(a) Measure of each exterior angle of a regular polygon with 9 sides = = 40º
9
360∞
(b) Measure of each exterior angle of a regular polygon with 15 sides = = 24º
15

EXERCISE 16.1

1. Two angles of a quadrilateral are 80º and 135º. The other two angles are equal. Find the other two angles.
2. The four angles of a quadrilateral are in the ratio 3 : 4 : 5 : 6. Find the angles.
3. Find x in each figure:

Q x G
80° 65° 95°
R
A H F
90°
P
45°
70°
x D
C S 130°
B 150° 80°
x
E
(a) (b) (c)

4. The sum of three angles of a quadrilateral is 5 times the fourth angle. Find the fourth angle.
5. Three angles of a quadrilateral are in the ratio 4 : 5 : 6. The sum A B
of the least and the greatest of these is 160º. Find the angles of x
the quadrilateral. 110°
6. The two adjacent angles of a quadrilateral are 80º and 120º. The 85°
other two angles are equal. Find them. D 60° y
7. Find x and y in the given figure. C
E
Types of Quadrilaterals

Let us discuss the various types of quadrilaterals and their properties.

Parallelogram
A quadrilateral whose opposite sides are parallel is a parallelogram.

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