Chapter 2.7, Problem 17PSC

To determine

To prove : The value of $\angle DBE={90}^0$ is to be proved

Explanation of Solution

Given information : The following information has been given

  $\overrightarrow{AB}\perp \overrightarrow{BC}$

  $\angle 1=\angle 3$

Formula used : linear addition of angles is used

Proof : We are given that $\overrightarrow{AB}\perp \overrightarrow{BC}$ , hence we know that

  $\angle ABC={90}^0$

Now, We can say that

  $\angle ABC=\angle ADB+\angle DBC=\angle 1+\angle DBC$

Further, we use $\angle 1=\angle 3$ in the previous equation. Hence, we get

  $\angle ABC=\angle 3+\angle DBC=\angle DBE$

Now, as $\angle ABC=\angle DBE$ , and $\angle ABC={90}^0$ , we can say that

  $\angle DBE={90}^0$

Hence, the desired angle is proved