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


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