Page 222 - Start Up Mathematics_8 (Non CCE)

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 6: In a quadrilateral LIVE, –L = 40º, –I = 60º, –V = 60º. I
Find –E. Is this quadrilateral convex or concave? L
Solution: In quadrilateral LIVE,
–L + –I + –V + –E = 360º

(sum of the four angles of a quadrilateral is 360º)
fi 40º + 60º + 60º + –E = 360º E V
fi 160º + –E = 360º fi –E = 360º – 160º = 200º
Since one angle of the quadrilateral LIVE is greater than 180°, it is a concave quadrilateral.
Example 7: Find the measure of each exterior angle of a regular polygon with: (a) 9 sides (b) 15 sides
(NCERT)
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 14.2

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 B
sum of the least and the greatest of these is 160º. Find the A x
angles of the quadrilateral. 110°
6. The two adjacent angles of a quadrilateral are 80º and 120º.
The other two angles are equal. Find them. 85° 60° y
7. Find x and y in the given figure. D
C
E

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