Mathematics

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

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

##### 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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Single Correct Medium Published on 09th 09, 2020
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