Question

The adjacent angles on a straight line are $(5x-6{)}^o$ and $7(x+6{)}^o$. Find the value of $x$.

Answer 1

Given that, ${(5x-6)}^o$ and ${7(x+6)}^o$ are adjacent angles on a straight line.

Since the sum of adjacent angles on a straight line $={180}^o$

We can write,, ${(5x-6)}^o+{7(x+6)}^o={180}^o$

$\Rightarrow 5x-6+7x+42=180$

$\Rightarrow 12x=180-36$

$\Rightarrow x=\frac{144}{12}$

$\Rightarrow x=12$

The adjacent angles are as follows:

${(5x-6)}^o=(5\times 12-6{)}^o=(60-6{)}^o={54}^o$

And, ${7(x+6)}^o=7(12+6{)}^o=7\times {18}^o={126}^o$