Construct a trapezium mice , where MI || CE,MI=5cm, IC=4cm, angle E =120 degrees and angle C=45 degrees

Answer :

We follow these steps , As :

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

$\angle$ M  + $\angle$ E  =  180$°$ , So

$\angle$ M  + 120$°$  =  180$°$

$\angle$ M = 60$°$
And
$\angle$ I  + $\angle$ C  =  180$°$ , So

$\angle$ I  + 45$°$  =  180$°$

$\angle$ I = 135$°$

Step 1  : Draw a line MI  =  5 cm 

Step 2 : Take any radius ( Less than half of MI )  and center " M "  draw an arc that intersect our line MI at " P " . With same radius and center " P "  draw another arc that intersect our previous arc at " Q " . Join MQ and extend it to  "R " we get MR .

Step 3 : We extend line MI to Z we get line segment " IZ " .Now take any radius ( Less than half of IZ )  and center " I "  draw a semicircle that intersect our line IZ 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 " F " .  Now with same radius and center " B " and " F " draw arcs these arcs intersect at " G "  .

Step 4 : Join IG that intersect semicircle at " H " . Now with same radius and center " A " and " H " draw arcs these arcs intersect at " J "  . Join line IJ and extend it to " Y "  we get line " IY " .

Step 5 : Take radius of 4 cm and center " I "  draw an arc that intersect line IY at " C " .


Step 6 :Take any radius ( Less than half of IC)  and center " C "  draw a semicircle that intersect our line IC at "S " . With same radius and center " S "  draw an arc that intersect our semicircle at " T " .With same radius and center " T "  draw another arc that intersect our semicircle at " U " .  Now with same radius and center " T " and " U " draw arcs these arcs intersect at " V "  .

Step 7 : Join CV  that intersect semicircle at " W " . Now with same radius and center " S " and " W " draw arcs these arcs intersect at " X "  . Join line CX and extend it that linet intersect line MR at " E "

We get required trapezium  MICE