Question

in the following figure AB||CD.find the value of x ​

Answer 1

Answer: 250°

Step-by-step explanation:

If AB||CD, draw BE such that <ABE = <BED = 35°

Also, Draw DF such that <CDF = <BFD = 75°

Now, in triangle EMD,

=> <MDE+<MED+<EMD = 180°

=> 75°+ 35°+<EMD = 180°

=>180°-110° = <EMD

=>70° = <EMD --(i)

Now, in triangle BMF,

=> <MBF+<MFB+<BMF = 180°

=> 35°+75°+<BMF = 180°

=> 180°-110° = <BMF

=> 70° = <BMF --(ii)

Also, in triangle BMF,

=> <MBF+<MFB = <EMF [Ext. Angle Prop.]

=> <EMF = 110° --(iii)

Now, for x

=> <BMF+<EMD+<EMF = x°

From (i), (ii) and (iii),

=> 70°+70°+110° = x°

=> x° = 250°