Chapter SR20, Problem 4P

Solution

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

  $x={12}^o$

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 $\angle ABD={(3x-4)}^0$

And $\angle DBC={(4x+10)}^0$

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

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

  $\begin{array}{c}$ {(3x-4)}^0+{(4x+10)}^0={90}^o$3x-4+4x+10=90\\ 7x+6=90\\ 7x=90-6\\ 7x=84\\ x=\frac{84}{7}\\ x=12\end{array}$

  $x={12}^o$