Question

construction of trapezium PQRS with PS=4.7cm, RS=8cm, angle P=120°,angleR= 45°

Answer 1

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

∠ P  + ∠ S  =  180° , So

∠ S  + 120°  =  180°

∠ 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 " . .....

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 "  . .

Step 4 : Take any radius ( Less than half of RS )  and center " S "  draw an arc that intersect our line RS at " G " .
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 " .

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

I hope it helps