4.2.1 Polygons, PT3 Practice


4.2.1 Polygons, 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

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