# 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$\xb0$ , So

$\angle $ S + 120$\xb0$ = 180$\xb0$

$\angle $ S = 60$\xb0$

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

**
**