We can say that the two triangles are identical, then, the angle GPK is equal to the angle KPH, then we write the following equation:
[tex]\begin{gathered} \angle GPK=\angle KPH \\ \\ 18x+5=14x+15 \\ \\ 4x=10 \\ \\ x=\frac{10}{4}=\frac{5}{2}=2.5 \end{gathered}[/tex]
Now we know the value of x, we can return to the equation and find the value of the angle GPK
[tex]\begin{gathered} \angle GPK=18x+5 \\ \\ \operatorname{\angle}GPK=18\cdot\frac{5}{2}+5 \\ \\ \operatorname{\angle}GPK=9\cdot5+5 \\ \\ \operatorname{\angle}GPK=45+5 \\ \\ \angle GPK=50 \end{gathered}[/tex]
Therefore, the measure of the angle GPK is equal to 50 degrees
