Mathematics

# In $\Delta ABC$ fig, $\angle x + \angle y + \angle z$ is equals :

$360^{\circ}$

##### SOLUTION
$x+\angle 1=180^{\circ}........(i)$ (Angles made on straight line $AB$)
$y+\angle 2=180^{\circ}........(i)$ (Angles made on straight line $BC$)
$z+\angle 3=180^{\circ}........(i)$ (Angles made on straight line $AC$)
$\Rightarrow x+y+z+\angle 1+\angle 2+\angle 3={ 180 }^{ \circ }+{ 180 }^{ \circ }+{ 180 }^{ \circ }\\ \Rightarrow x+y+z+\angle 1+\angle 2+\angle 3={ 540 }^{ \circ }$
Now in $\triangle ABC$ , using angle sum property
$\angle 1+\angle 2+\angle 3=180^{\circ}$
Substituting in the above equation
$\Rightarrow x+y+z+{ 180 }^{ \circ }={ 540 }^{ \circ }\\ \Rightarrow x+y+z={ 360 }^{ \circ }$

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Single Correct Medium Published on 09th 09, 2020
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