Mathematics

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


ANSWER

$$360^{\circ}$$


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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