Question

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

Answer 1

Given: $x^o$ and ${(2x-27)}^o$ are adjacent angles on a straight line.

Now, $x^o+{(2x-27)}^o={180}^o$ ...(Since adjacent angles on a straight line $={180}^o$)

$\Rightarrow 3x=180+27$

$\Rightarrow 3x=207$

$\Rightarrow x=\frac{207}{3}$

$\Rightarrow x=69$

The ajacent angles are as follows:

$x^o={69}^o=$ Smallest angle

And, ${2x-27}^o=2\times 69-27=138-27={111}^o$