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

We follow these steps , As :

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

$\angle $ M + $\angle $ E = 180$\xb0$ , So

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

$\angle $ M = 60$\xb0$

And

$\angle $ I + $\angle $ C = 180$\xb0$ , So

$\angle $ I + 45$\xb0$ = 180$\xb0$

$\angle $ I = 135$\xb0$

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

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