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Gel · Answer 1 · 2023-05-25T20:53:56+0000

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:

$\begin{gathered} \angle GPK=\angle KPH \\ \\ 18x+5=14x+15 \\ \\ 4x=10 \\ \\ x=(10)/(4)=(5)/(2)=2.5 \end{gathered}$

Now we know the value of x, we can return to the equation and find the value of the angle GPK

$\begin{gathered} \angle GPK=18x+5 \\ \\ \operatorname{\angle}GPK=18\cdot(5)/(2)+5 \\ \\ \operatorname{\angle}GPK=9\cdot5+5 \\ \\ \operatorname{\angle}GPK=45+5 \\ \\ \angle GPK=50 \end{gathered}$

Therefore, the measure of the angle GPK is equal to 50 degrees

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