Chapter 7.1, Problem 6PSA

To determine

To calculate: Measure of $\angle O$

Answer to Problem 6PSA

Measure of $\angle O$ is $48°$ .

Explanation of Solution

Given information : Here, we have given that $\angle ORS=(4x+6)°$ , $\angle P=(x+24)°$ and $\angle O=(2x+4)°$

Formula used : Measure of Exterior Angle of a triangle is equal to sum of two opposite interior angles of that triangle.

Calculation: According to the figure, $\angle ORS$ is the exterior angle and $\angle P$ and $\angle O$ are the two interior angles at the opposite side of exterior angle.

  $\begin{array}{l}\Rightarrow \angle ORS=\angle P+\angle O\\ \Rightarrow (4x+6)°=(x+24)°+(2x+4)°\\ \Rightarrow (4x+6)°=(3x+28)°\\ \Rightarrow (4x-3x)°=(28-6)°\\ \Rightarrow x=22°\end{array}$

Now, putting $x=22°$ in $\angle O=(2x+4)°$ ,

  $\begin{array}{l}\Rightarrow \angle O=\left[2(22)+4\right]\\ \Rightarrow \angle O=(44+4)°\\ \Rightarrow \angle O=48°\end{array}$