Question

Let point P be in the interior of

Answer 1

Let us draw the figure to understand it

Since m

Since m

Since m

Since m

Then add (9x + 11) and (7x - 5) and equate the sum by 102

$(9x+11)+(7x-5)=102$

Add the like terms on the left side

$\begin{gathered} (9x+7x)+(11-5)=102 \\ 16x+6=102 \end{gathered}$

Subtract 6 from both sides

$\begin{gathered} 16x+6-6=102-6 \\ 16x=96 \end{gathered}$

Divide both sides by 16

$\begin{gathered} \frac{16x}{16}=\frac{96}{16} \\ x=6 \end{gathered}$

Now to find the measure of angle RBP substitute x by 6 in its measure

$\begin{gathered} m\angle RBP=9(6)+11 \\ m\angle RBP=54+11 \\ m\angle RBP=\mathring{65} \end{gathered}$