Chapter SR20, Problem 6P

Solution

  $\angle ABD$ and $\angle DBC$ are complementary angles. Find the value of x.

  $x=7^o$

Given:

The given angle.

  

Concept Used:

• Two angles are complementary angles if the sum of their measures is ${90}^o$ .

Calculation:

The given angle is −

  

As $\angle ABD={(7x+5)}^0$

And $\angle DBC={(5x+1)}^0$

  $\angle ABD$ and $\angle DBC$ are complementary angles, their sum is ${90}^o$ .

So $\angle ABD+\angle DBC={90}^o$

  $\begin{array}{c}$ {(7x+5)}^0+{(5x+1)}^0={90}^o$7x+5+5x+1=90\\ 12x+6=90\\ 12x=90-6\\ 12x=84\\ x=\frac{84}{12}\\ x=7\end{array}$

  $x=7^o$