Chapter SR20, Problem 8P

Solution

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

  $x={52}^o$

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 $\angle ABD={(x-28)}^0$

And $\angle DBC=3x^0$

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

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

  $\begin{array}{c}$ {(x-28)}^0+3x^0={180}^o$x-28+3x=180\\ 4x-28=180\\ 4x=180+28\\ 4x=208\\ x=\frac{208}{4}\\ x=52\end{array}$

  $x={52}^o$