Chapter 2.6, Problem 4ST2

To determine

To express: the measures of all angles in terms of $t.$ .

Answer to Problem 4ST2

  $m\angle 4=90-t,m\angle 5=t,m\angle 6=90-t$

Explanation of Solution

Given information:

  $m\angle 3=t$

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,

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

Hence, $m\angle 4=90-t,m\angle 5=t,m\angle 6=90-t$ .