Mathematics

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

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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