Understanding Quadrilaterals
Exercise 3.2
Question 1: Find x in the following figures:
Answer 1:
(a) Here, 125o+m=180o [Linear pair]
m=180o-125o = 55o
and 125o+n =180o [Linear pair]
n =180o-125o = 55o
Exterior angle xo = Sum of opposite interior angles
xo = 55o+55o =110o
(b) Sum of angles of a pentagon = (n - 2)x180o
= (5 - 2)x180o
= 3x180o = 540o
By linear pairs of angles,
Adding eq. (i), (ii), (iii), (iv) and (v),
Question 2:
Find the measure of each exterior angle of a regular polygon of:
(a) 9 sides
(b) 15 sides
Answer 2:
(i) Sum of angles of a regular polygon = (n-2)x180o
= (9-2)x180o = 7x180o =1260o
Each interior angle= Sum of interior angles / Number of sides =1260o/9 =140o
Each exterior angle = 180o-140o = 40o
(ii) Sum of exterior angles of a regular polygon = 360o
Each interior angle = Sum of interior angles/Number of sides = 360o/15 =24o
Question 3:
How many sides does a regular polygon have, if the measure of an exterior angle is 24o?
Answer 3:
Let number of sides be n.
Hence, the regular polygon has 15 sides.
Question 4:
How many sides does a regular polygon have if each of its interior angles is 165?
Answer 4:
Let number of sides be n.
Exterior angle = 180o-165o=15o
Sum of exterior angles of a regular polygon = 360o
Hence, the regular polygon has 24 sides.
Question 5:
(a) Is it possible to have a regular polygon with of each exterior angle as 22o?
(b) Can it be an interior angle of a regular polygon? Why?
Answer 5:
(a) No. (Since 22 is not a divisor of 360o )
(b) No, (Because each exterior angle is 180o - 22o =158o, which is not a divisor of 360o )
Question 6:
(a) What is the minimum interior angle possible for a regular polygon? Why?
(b) What is the maximum exterior angle possible for a regular polygon?
Answer 6:
(a) The equilateral triangle being a regular polygon of 3 sides has the least measure of an interior angle of 60o .
Sum of all the angles of a triangle = 180o
x+x+x= 180
3x=1800
x=60o
(b) By (a), we can observe that the greatest exterior angle is 1800 - 600 =1200.
1. What is a quadrilateral? |
2. What are the types of quadrilaterals? |
3. How do you identify a parallelogram? |
4. What is the difference between a rhombus and a square? |
5. How can we calculate the area of a quadrilateral? |
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