2.2.2 Polygons II, PT3 Practice


Question 6:
In diagram below, PQRSTU is a regular hexagon QUV is a straight line.



Find the value of x.

Solution:
Each interior angle = ( 62 )× 180 o 6 = 120 o PUQ= 180 o 120 o 2 = 30 o  (PUQ is a isosceles triangle) x o = 180 o 30 o = 150 o x=150



Question 7:
In diagram below, PQRSTU is a hexagon. UPE, PQF, QRG, RSH and UTJ are straight lines.



Find the value of x.

Solution:
Sum of all the exterior angles of any polygon= 360 o 25 o +3 x o +2 x o + 40 o + 75 o + 55 o = 360 o 5 x o + 195 o = 360 o   5 x o = 360 o 195 o    = 165 o x o = 165 o ÷5    = 33 o  x=33



Question 8:
In Diagram below, A, B, C, D and E are vertices of a 9 sided regular polygon.

Find the value of x.

Solution:
Exterior angle = 360 o 9 = 40 o Interior angle= 180 o 40 o = 140 o Sum of interior angles of pentagon ABCDE =( 52 )× 180 o = 540 o x o + 140 o + 140 o + 140 o + x o = 540 o 2 x o = 540 o 420 o  = 120 o    x o = 60 o    x=60


2.2.1 Polygons II, PT3 Practice


2.2.1 Polygons II, PT3 Practice

Question 1:
Diagram below shows a pentagon PQRST. TPU and RSV are straight lines.
Find the value of x.

Solution:
Sum of interior angles of a pentagon =( 52 )× 180 o =3× 180 o = 540 o TSR= 180 o 70 o           = 110 o TPQ= 180 o 85 o           = 95 o x o = 540 o ( 110 o + 105 o + 115 o + 95 o )     = 540 o 425 o     = 115 o    x=115


Question 2:
In Diagram below, PQRSTU is a hexagon. APQ and BTS are straight lines.
Find the value of x + y.

Solution:

Q P U = 180 o 160 o = 20 o Reflex P U T = 360 o 80 o = 280 o U T S = 180 o 120 o = 60 o T S R = 180 o 35 o = 145 o Sum of interior angles of a hexagon = ( 6 2 ) × 180 o = 720 o x o + y o + 145 o + 60 o + 280 o + 20 o = 720 o x o + y o = 720 o 505 o = 215 o x + y = 215


Question 3:
Diagram below shows a regular hexagon PQRSTU. PUV is a straight line.
Find the value of x + y.

Solution:
Size of each interior angle of a regular hexagon = ( 6 2 ) × 180 o 6 = 120 o x o = 180 o 120 o 2 = 30 o y o = 180 o 120 o = 60 o x o + y o = 30 o + 60 o = 90 o x + y = 90


Question 4:
In the diagram below, KLMNP is a regular pentagon. LKS and MNQ are straight lines.
Find the value of x + y.
 
Solution:
Size of each interior angle of a regular pentagon = ( 5 2 ) × 180 o 5 = 108 o P K S = P N Q = 180 o 108 o = 72 o Reflex angle K P N = 360 o 108 o = 252 o

Sum of interior angles of a hexagon = ( 6 2 ) × 180 o = 720 o x o + y o + 72 o + 252 o + 72 o + 100 o = 720 o x o + y o = 720 o 496 o = 224 o x + y = 224


Question 5:
In Diagram below, PQR is an isosceles triangle and PRU is a straight line.
Find the value of x + y.

Solution:
x o = 180 o 20 o 20 o = 140 o P R S = 180 o 110 o = 70 o y o + 85 o + 75 o + 70 o = 360 o y o + 230 o = 360 o y o = 130 o x o + y o = 140 o + 130 o = 270 o x + y = 270
 

2.1 Polygons II


2.1 Polygons II
 
2.1.1 Regular Polygons
1.  A regular polygon is a polygon where
(a) all its sides are of equal length, and
(b) all its interior angles are of equal size.

2. The number of axis of symmetry of a regular polygon is equal to its number of sides.

Example:


2.1.2 Exterior and Interior Angles of Polygons
1. The exterior and interior angles at a vertex of a polygon is supplementary.

2. The sum of interior angles of an n-sided polygon is  ( n 2 ) × 180 o  

3. 
Each interior angle of a regular n-sided polygon is
( n 2 ) × 180 o n

4. 
The sum of all exterior angles of a polygon is 360o.

5. Each exterior angle of a regular n-sided polygon is 
360 o n