Chapter SR20, Problem 7P

Solution

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

  $x={23}^o$

Given:

The given angle.

  

Concept Used:

• Two angles are supplementary angles if the sum of their measures is ${180}^o$ .

Calculation:

The given angle is −

  

As $\angle ABD={(4x+17)}^0$

And $\angle DBC={(3x+2)}^0$

  $\angle ABD$ and $\angle DBC$ are supplementary angles, their sum is ${180}^o$ .

So $\angle ABD+\angle DBC={180}^o$

  $\begin{array}{c}$ {(4x+17)}^0+{(3x+2)}^0={180}^o$4x+17+3x+2=180\\ 7x+19=180\\ 7x=180-19\\ 7x=161\\ x=\frac{161}{7}\\ x=23\end{array}$

  $x={23}^o$