Chapter 1.5, Problem 18PSB

To determine

To find: The $m\angle FOG$ .

Answer to Problem 18PSB

  $m\angle FOG=80°$

Explanation of Solution

Given:

  

  $\begin{array}{l}\angle RPS=23°50\text{'}\\ \overrightarrow{OG}\text{and }\overrightarrow{OH}\text{divide straight angle }\angle FOJ\\ \text{into three angles whose measures are in the ratio 4:3:2}\end{array}$

Concept Used:

Sum of measure of straight angle is 180 degrees.

Calculation:

Here, we have

  $\begin{array}{l}\because \angle FOJ=\angle FOG+\angle GOH+\angle HOJ\\ \Rightarrow 180°=4x+3x+2x\\ \Rightarrow 180°=9x\\ \Rightarrow 20°=x\\ \therefore x=20°\\ \Rightarrow \angle FOG=4\times 20°=80°\\ \Rightarrow m\angle FOG=80°\end{array}$

Conclusion:

  $m\angle FOG=80°$