Chapter 1, Problem 9RP

To determine

To calculate: Whether $\angle NOR$ and $\angle POS$ can both be right angles or not

Answer to Problem 9RP

No, both of the angles cannot be right angles.

Explanation of Solution

Given information: The following measures of angles can be calculated from the given drawing

  $\angle NOP={60}^0$

  $\angle ROS={70}^0$

  $\angle NOR=\angle NOP+\angle POR$

  $\angle POS=\angle POR+\angle ROS$

Formula used: Simple addition of angles has been done

Calculation: We try to do the following eliminations

Now, using the last two statements, we try to eliminate $\angle POR$

Thus,

  $\angle ROS+\angle NOR=\angle NOP+\angle POS$

Now, we substitute the values of $\angle NOP={60}^0$ and $\angle ROS={70}^0$ in the previous equation

Thus,

  ${70}^0+\angle NOR={60}^0+\angle POS$

Now, simplifying it further we get

  $\angle POS=\angle NOR+{10}^0$

Thus, we can clearly see that $\angle NOR$ and $\angle POS$ both cannot be right angles