Chapter SR20, Problem 5P

Solution

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

  $x={16}^o$

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 $\angle ABD={(3x-18)}^0$

And $\angle DBC={(5x-20)}^0$

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

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

  $\begin{array}{c}$ {(3x-18)}^0+{(5x-20)}^0={90}^o$3x-18+5x-20=90\\ 8x-38=90\\ 8x=90+38\\ 8x=128\\ x=\frac{128}{8}\\ x=16\end{array}$

  $x={16}^o$