write the steps for construction in which triangle XYZ in which XY =6CM , angle ZXY = 60 degree , angle ZYX= 45 degree ?

Answer :

We follow these steps to construct Triangle XYZ from given formation  .

Step 1 :  Draw a line XY  =   6 cm

Step 2 :  Now take any radius ( Less than half of XY ) and take center  " X "  draw an arc that intersect our line XY at  " A " , With same radius and center is " A "  draw another arc that intersect our previous arc at "  B " .

Step 3 :  Draw a line XB and extend it  . So ,  $\angle$ BXY  = 60$°$

Step 4 :  Now take any radius ( Less than half of XY ) and take center  " Y "  draw an arc that intersect our line XY at  " C " , With same radius and center is " C "  draw another arc that intersect our previous arc at "  D " and again with same radius and center " D "  draw another arc that intersect our main arc at " E "

Step 5 :  With same radius and take center " D " and " E "  we draw two arcs that intersect at " F " . Now join YF  , line YF intersect at main arc at  "  G "

Step 6 : With same radius and take center " C  " and " G "  we draw two arcs that intersect at " H ".

Step 7 :  Draw a line YH and extend it  . So ,  $\angle$ HYX = 45$°$

Line XB and YH intersect at  "  Z "  , This is our required triangle XYZ  , Here XY  =  6 cm  ,   $\angle$ ZXY  = 60$°$  And $\angle$ ZYX = 45$°$

As ( $\angle$ HYX = 45$°$  =  $\angle$ ZYX = 45$°$ Same angles And $\angle$ BXY = 60$°$  =  $\angle$ ZXY  = 60$°$  )