Mathematics

The measures of two adjacent angles on a straight line are $$x^o$$ and $$(2x-27)^o$$. Find smallest angle


ANSWER

69


SOLUTION
Given that $${ x }^{ o }$$ and $${ \left( 2x-27 \right)  }^{ o }$$ are adjacent angles on a straight line.
Now, $${ x }^{ o }+{ \left( 2x-27 \right)  }^{ o }={ 180 }^{ o }$$      ...(Since adjacent angles on a straight line $$={ 180 }^{ o }$$)
$$ \Rightarrow 3x=180+27$$
$$ \Rightarrow 3x=207 $$
$$\Rightarrow x=\cfrac { 207 }{ 3 }  $$
$$\Rightarrow x=69$$ 
The ajacent angles are as follows:
$$ { x }^{ o }={ 69 }^{ o }$$ 
And, $${ 2x-27 }^{ o }=2\times 69-27=138-27={ 111 }^{ o }$$
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