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
Questions 120418
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