Mathematics

In each of the following figure AB || CD. Find the value of x in each case.


SOLUTION
Draw a line $$EF$$ perpendicular to $$AB$$ and $$CD$$ passing through $$M$$
In $$\triangle BME$$ 
$$\angle BME+\angle MBE+\angle BEM={180}^{\circ}$$ (Angle sum proprerty)
$$\angle BME+{ 35 }^{ \circ  }+{ 90 }^{ \circ  }={ 180 }^{ \circ  }\\ \angle BME={ 180 }^{ \circ  }-{ 125 }^{ \circ  }\\ \angle BME={ 45 }^{ \circ  }$$
In $$\triangle DMF$$
$$\angle DMF+\angle MDF+\angle MFD={180}^{\circ}$$ (Angle sum property )
$$\angle DMF+{ 75 }^{ \circ  }+{ 90 }^{ \circ  }={ 180 }^{ \circ  }\\ \angle DMF={ 180 }^{ \circ  }-{ 165 }^{ \circ  }\\ \angle DMF={ 15 }^{ \circ  }$$
$$x=\angle DMF+\angle BME+\angle EMF$$
$$x={ 15 }^{ \circ  }+{ 45 }^{ \circ  }+{ 180 }^{ \circ  }\\ x={ 240 }^{ \circ  }$$

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Subjective Medium Published on 09th 09, 2020
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