Mathematics

Find the values of the angles x, y and z in each of the following:


ANSWER

$$i)x=55$$ $$y=125$$ $$z=125$$  $$ii)x=115$$ $$y=140$$ $$z=40$$


SOLUTION
i)$$x={ 55 }^{ \circ  }\quad (vertically\quad opposite\quad angles,x={ 55 }^{ \circ  }and\quad y=z)$$
$$ x+y={ 180 }^{ \circ  }\quad (sum\quad of\quad angles\quad on\quad a\quad straight\quad line={ 180 }^{ \circ  })$$
$$\implies\quad y=180-55={ 125 }^{ \circ  }$$
$$ \because y=z\quad (vertically\quad opposite)$$
$$\implies\quad z={ 125 }^{ \circ  }=y\\ x={ 55 }^{ \circ  }$$
ii)$$z={ 40 }^{ \circ  }\quad (vertically\quad opposite\quad angles)$$
$$ x+{ 25 }^{ \circ  }=y\quad (vertically\quad opposite\quad angles)$$
$$ y+{ 40 }^{ \circ  }={ 180 }^{ \circ  }\quad (\because Sum\quad of\quad angles\quad on\quad a\quad straight\quad line={ 180 }^{ \circ  })$$
$$\implies\quad y={ 140 }^{ \circ  }$$
$$\implies\quad x+25=y$$
$$\implies\quad x=140-25={ 115 }^{ \circ  }$$
Hence answer$$(i)x=55$$ $$y=125$$ $$z=125$$ 
$$(ii)x=115$$ $$y=140$$ $$z=40$$
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