Chapter 2.6, Problem 3ST2

To determine

To find: the values of the $m\angle 4,m\angle 5,m\angle 6$ .

Answer to Problem 3ST2

  $m\angle 4=53,m\angle 5=37,m\angle 6=53$

Explanation of Solution

Given information:

  $m\angle 3=37$

And the given figure is as follows.

  $\overrightarrow{OB}\perp l,\overrightarrow{OA}\perp \overrightarrow{OC}$

As per the definition of perpendicular lines, the perpendicular lines intersect to form a

right angle.

So, from given data,

  $\begin{array}{l}m\angle 3+m\angle 4=90\\ 37+m\angle 4=90\\ m\angle 4=53\\ m\angle 4+m\angle 5=90\\ m\angle 5=90-53\\ m\angle 5=37\\ m\angle 5+m\angle 6=90\\ m\angle 6=90-37\\ m\angle 6=53\end{array}$

Hence, $m\angle 4=53,m\angle 5=37,m\angle 6=53$ .