# Construct a Trapezium PQRS in which PQ is Parallel to RS . Given PS=4.5cm, RS=8cm, Angle P=120 degree, angle R= 45 degree.

We follow these steps , As :

We know in trapezium " Adjacent angles  along the sides are supplementary. So

$\angle$ P  + $\angle$ S  =  180$°$ , So

$\angle$ S  + 120$°$  =  180$°$

$\angle$ S = 60$°$

Step 1  : Draw a line RS  =  8 cm

Step 2 : Now take any radius ( Less than half of RS )  and center " R "  draw a semicircle that intersect our line RS at "A " . With same radius and center " A "  draw an arc that intersect our semicircle at " B " .With same radius and center " B "  draw another arc that intersect our semicircle at " C " .  Now with same radius and center " B " and " C " draw arcs these arcs intersect at " D "  .

Step 3 : Join RD that intersect semicircle at " E " . Now with same radius and center " A " and " E " draw arcs these arcs intersect at " F "  . Join line RF and extend it to " X "  we get line " RX " .

Step 4 : Take any radius ( Less than half of RS )  and center " S "  draw an arc that intersect our line RS at " G " . With same radius and center " G "  draw another arc that intersect our previous arc at " H " . Join SH and extend it to  " Y " we get SY .

Step 5 : Take radius of 4.5 cm and center " S "  draw an arc that intersect line SY at " P " .

Step 6 :Take any radius ( Less than half of PS)  and center " P "  draw a semicircle that intersect our line PS at " I " . With same radius and center " I "  draw an arc that intersect our semicircle at " J " .With same radius and center " J "  draw another arc that intersect our semicircle at " K " .

Step 7 : Join PK that intersect  our line " RX " at " Q " . We get required trapezium  PQRS

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