We are given the measures of two angles in the form of linear equations. According to the graph, the measure of both angles is 90°. therefore, we can establish an equation and find the variable "p", from there we can replace that variable in the equation for the required angle.
The sum of the angles is:
[tex]7p+16+4p+30=90[/tex]we add like terms, like this
[tex]11p+46=90[/tex]substracting 46 on both sides we get
[tex]\begin{gathered} 11p+46-46=90-46 \\ 11p=44 \end{gathered}[/tex]Dividing each side by 11
[tex]p=\frac{44}{11}=4[/tex]Now that we have the value for "p" we can replace it in the equation for angle PTH, like this
[tex]\angle PTH=4p+30[/tex][tex]\angle PTH=4(4)+30=46[/tex]Therefore angle PTH is 46
